1 // SPDX-License-Identifier: GPL-2.0-or-later <<
2 /* 1 /*
3 Red Black Trees 2 Red Black Trees
4 (C) 1999 Andrea Arcangeli <andrea@suse.de> 3 (C) 1999 Andrea Arcangeli <andrea@suse.de>
5 (C) 2002 David Woodhouse <dwmw2@infradead.o 4 (C) 2002 David Woodhouse <dwmw2@infradead.org>
6 (C) 2012 Michel Lespinasse <walken@google.c 5 (C) 2012 Michel Lespinasse <walken@google.com>
7 6
>> 7 This program is free software; you can redistribute it and/or modify
>> 8 it under the terms of the GNU General Public License as published by
>> 9 the Free Software Foundation; either version 2 of the License, or
>> 10 (at your option) any later version.
>> 11
>> 12 This program is distributed in the hope that it will be useful,
>> 13 but WITHOUT ANY WARRANTY; without even the implied warranty of
>> 14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
>> 15 GNU General Public License for more details.
>> 16
>> 17 You should have received a copy of the GNU General Public License
>> 18 along with this program; if not, write to the Free Software
>> 19 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
8 20
9 linux/lib/rbtree.c 21 linux/lib/rbtree.c
10 */ 22 */
11 23
12 #include <linux/rbtree_augmented.h> 24 #include <linux/rbtree_augmented.h>
13 #include <linux/export.h> 25 #include <linux/export.h>
14 26
15 /* 27 /*
16 * red-black trees properties: https://en.wik !! 28 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
17 * 29 *
18 * 1) A node is either red or black 30 * 1) A node is either red or black
19 * 2) The root is black 31 * 2) The root is black
20 * 3) All leaves (NULL) are black 32 * 3) All leaves (NULL) are black
21 * 4) Both children of every red node are bla 33 * 4) Both children of every red node are black
22 * 5) Every simple path from root to leaves c 34 * 5) Every simple path from root to leaves contains the same number
23 * of black nodes. 35 * of black nodes.
24 * 36 *
25 * 4 and 5 give the O(log n) guarantee, since 37 * 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 38 * 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 39 * 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 40 * 5), then the longest possible path due to 4 is 2B.
29 * 41 *
30 * We shall indicate color with case, where b 42 * We shall indicate color with case, where black nodes are uppercase and red
31 * nodes will be lowercase. Unknown color nod 43 * nodes will be lowercase. Unknown color nodes shall be drawn as red within
32 * parentheses and have some accompanying tex 44 * parentheses and have some accompanying text comment.
33 */ 45 */
34 46
35 /* <<
36 * Notes on lockless lookups: <<
37 * <<
38 * All stores to the tree structure (rb_left a <<
39 * WRITE_ONCE(). And we must not inadvertently <<
40 * tree structure as seen in program order. <<
41 * <<
42 * These two requirements will allow lockless <<
43 * correct iteration mind you, tree rotations <<
44 * miss entire subtrees. <<
45 * <<
46 * But they do guarantee that any such travers <<
47 * and that it will indeed complete -- does no <<
48 * <<
49 * It also guarantees that if the lookup retur <<
50 * one. But not returning an element does _NOT <<
51 * <<
52 * NOTE: <<
53 * <<
54 * Stores to __rb_parent_color are not importa <<
55 * are left undone as of now. Nor did I check <<
56 * pointers. <<
57 */ <<
58 <<
59 static inline void rb_set_black(struct rb_node 47 static inline void rb_set_black(struct rb_node *rb)
60 { 48 {
61 rb->__rb_parent_color += RB_BLACK; !! 49 rb->__rb_parent_color |= RB_BLACK;
62 } 50 }
63 51
64 static inline struct rb_node *rb_red_parent(st 52 static inline struct rb_node *rb_red_parent(struct rb_node *red)
65 { 53 {
66 return (struct rb_node *)red->__rb_par 54 return (struct rb_node *)red->__rb_parent_color;
67 } 55 }
68 56
69 /* 57 /*
70 * Helper function for rotations: 58 * Helper function for rotations:
71 * - old's parent and color get assigned to ne 59 * - old's parent and color get assigned to new
72 * - old gets assigned new as a parent and 'co 60 * - old gets assigned new as a parent and 'color' as a color.
73 */ 61 */
74 static inline void 62 static inline void
75 __rb_rotate_set_parents(struct rb_node *old, s 63 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
76 struct rb_root *root, 64 struct rb_root *root, int color)
77 { 65 {
78 struct rb_node *parent = rb_parent(old 66 struct rb_node *parent = rb_parent(old);
79 new->__rb_parent_color = old->__rb_par 67 new->__rb_parent_color = old->__rb_parent_color;
80 rb_set_parent_color(old, new, color); 68 rb_set_parent_color(old, new, color);
81 __rb_change_child(old, new, parent, ro 69 __rb_change_child(old, new, parent, root);
82 } 70 }
83 71
84 static __always_inline void 72 static __always_inline void
85 __rb_insert(struct rb_node *node, struct rb_ro 73 __rb_insert(struct rb_node *node, struct rb_root *root,
86 void (*augment_rotate)(struct rb_n 74 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
87 { 75 {
88 struct rb_node *parent = rb_red_parent 76 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
89 77
90 while (true) { 78 while (true) {
91 /* 79 /*
92 * Loop invariant: node is red !! 80 * Loop invariant: node is red
>> 81 *
>> 82 * If there is a black parent, we are done.
>> 83 * Otherwise, take some corrective action as we don't
>> 84 * want a red root or two consecutive red nodes.
93 */ 85 */
94 if (unlikely(!parent)) { !! 86 if (!parent) {
95 /* <<
96 * The inserted node i <<
97 * first node, or we r <<
98 * are no longer viola <<
99 */ <<
100 rb_set_parent_color(no 87 rb_set_parent_color(node, NULL, RB_BLACK);
101 break; 88 break;
102 } !! 89 } else if (rb_is_black(parent))
103 <<
104 /* <<
105 * If there is a black parent, <<
106 * Otherwise, take some correc <<
107 * per 4), we don't want a red <<
108 * consecutive red nodes. <<
109 */ <<
110 if(rb_is_black(parent)) <<
111 break; 90 break;
112 91
113 gparent = rb_red_parent(parent 92 gparent = rb_red_parent(parent);
114 93
115 tmp = gparent->rb_right; 94 tmp = gparent->rb_right;
116 if (parent != tmp) { /* par 95 if (parent != tmp) { /* parent == gparent->rb_left */
117 if (tmp && rb_is_red(t 96 if (tmp && rb_is_red(tmp)) {
118 /* 97 /*
119 * Case 1 - no !! 98 * Case 1 - color flips
120 * 99 *
121 * G 100 * G g
122 * / \ 101 * / \ / \
123 * p u 102 * p u --> P U
124 * / 103 * / /
125 * n !! 104 * n N
126 * 105 *
127 * However, si 106 * However, since g's parent might be red, and
128 * 4) does not 107 * 4) does not allow this, we need to recurse
129 * at g. 108 * at g.
130 */ 109 */
131 rb_set_parent_ 110 rb_set_parent_color(tmp, gparent, RB_BLACK);
132 rb_set_parent_ 111 rb_set_parent_color(parent, gparent, RB_BLACK);
133 node = gparent 112 node = gparent;
134 parent = rb_pa 113 parent = rb_parent(node);
135 rb_set_parent_ 114 rb_set_parent_color(node, parent, RB_RED);
136 continue; 115 continue;
137 } 116 }
138 117
139 tmp = parent->rb_right 118 tmp = parent->rb_right;
140 if (node == tmp) { 119 if (node == tmp) {
141 /* 120 /*
142 * Case 2 - no !! 121 * Case 2 - left rotate at parent
143 * the parent' <<
144 * 122 *
145 * G 123 * G G
146 * / \ 124 * / \ / \
147 * p U - 125 * p U --> n U
148 * \ 126 * \ /
149 * n 127 * n p
150 * 128 *
151 * This still 129 * This still leaves us in violation of 4), the
152 * continuatio 130 * continuation into Case 3 will fix that.
153 */ 131 */
154 tmp = node->rb !! 132 parent->rb_right = tmp = node->rb_left;
155 WRITE_ONCE(par !! 133 node->rb_left = parent;
156 WRITE_ONCE(nod <<
157 if (tmp) 134 if (tmp)
158 rb_set 135 rb_set_parent_color(tmp, parent,
159 136 RB_BLACK);
160 rb_set_parent_ 137 rb_set_parent_color(parent, node, RB_RED);
161 augment_rotate 138 augment_rotate(parent, node);
162 parent = node; 139 parent = node;
163 tmp = node->rb 140 tmp = node->rb_right;
164 } 141 }
165 142
166 /* 143 /*
167 * Case 3 - node's unc !! 144 * Case 3 - right rotate at gparent
168 * the parent's left c <<
169 * 145 *
170 * G 146 * G P
171 * / \ / 147 * / \ / \
172 * p U --> n 148 * p U --> n g
173 * / 149 * / \
174 * n 150 * n U
175 */ 151 */
176 WRITE_ONCE(gparent->rb !! 152 gparent->rb_left = tmp; /* == parent->rb_right */
177 WRITE_ONCE(parent->rb_ !! 153 parent->rb_right = gparent;
178 if (tmp) 154 if (tmp)
179 rb_set_parent_ 155 rb_set_parent_color(tmp, gparent, RB_BLACK);
180 __rb_rotate_set_parent 156 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
181 augment_rotate(gparent 157 augment_rotate(gparent, parent);
182 break; 158 break;
183 } else { 159 } else {
184 tmp = gparent->rb_left 160 tmp = gparent->rb_left;
185 if (tmp && rb_is_red(t 161 if (tmp && rb_is_red(tmp)) {
186 /* Case 1 - co 162 /* Case 1 - color flips */
187 rb_set_parent_ 163 rb_set_parent_color(tmp, gparent, RB_BLACK);
188 rb_set_parent_ 164 rb_set_parent_color(parent, gparent, RB_BLACK);
189 node = gparent 165 node = gparent;
190 parent = rb_pa 166 parent = rb_parent(node);
191 rb_set_parent_ 167 rb_set_parent_color(node, parent, RB_RED);
192 continue; 168 continue;
193 } 169 }
194 170
195 tmp = parent->rb_left; 171 tmp = parent->rb_left;
196 if (node == tmp) { 172 if (node == tmp) {
197 /* Case 2 - ri 173 /* Case 2 - right rotate at parent */
198 tmp = node->rb !! 174 parent->rb_left = tmp = node->rb_right;
199 WRITE_ONCE(par !! 175 node->rb_right = parent;
200 WRITE_ONCE(nod <<
201 if (tmp) 176 if (tmp)
202 rb_set 177 rb_set_parent_color(tmp, parent,
203 178 RB_BLACK);
204 rb_set_parent_ 179 rb_set_parent_color(parent, node, RB_RED);
205 augment_rotate 180 augment_rotate(parent, node);
206 parent = node; 181 parent = node;
207 tmp = node->rb 182 tmp = node->rb_left;
208 } 183 }
209 184
210 /* Case 3 - left rotat 185 /* Case 3 - left rotate at gparent */
211 WRITE_ONCE(gparent->rb !! 186 gparent->rb_right = tmp; /* == parent->rb_left */
212 WRITE_ONCE(parent->rb_ !! 187 parent->rb_left = gparent;
213 if (tmp) 188 if (tmp)
214 rb_set_parent_ 189 rb_set_parent_color(tmp, gparent, RB_BLACK);
215 __rb_rotate_set_parent 190 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
216 augment_rotate(gparent 191 augment_rotate(gparent, parent);
217 break; 192 break;
218 } 193 }
219 } 194 }
220 } 195 }
221 196
222 /* 197 /*
223 * Inline version for rb_erase() use - we want 198 * Inline version for rb_erase() use - we want to be able to inline
224 * and eliminate the dummy_rotate callback the 199 * and eliminate the dummy_rotate callback there
225 */ 200 */
226 static __always_inline void 201 static __always_inline void
227 ____rb_erase_color(struct rb_node *parent, str 202 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
228 void (*augment_rotate)(struct rb_node 203 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
229 { 204 {
230 struct rb_node *node = NULL, *sibling, 205 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
231 206
232 while (true) { 207 while (true) {
233 /* 208 /*
234 * Loop invariants: 209 * Loop invariants:
235 * - node is black (or NULL on 210 * - node is black (or NULL on first iteration)
236 * - node is not the root (par 211 * - node is not the root (parent is not NULL)
237 * - All leaf paths going thro 212 * - All leaf paths going through parent and node have a
238 * black node count that is 213 * black node count that is 1 lower than other leaf paths.
239 */ 214 */
240 sibling = parent->rb_right; 215 sibling = parent->rb_right;
241 if (node != sibling) { /* nod 216 if (node != sibling) { /* node == parent->rb_left */
242 if (rb_is_red(sibling) 217 if (rb_is_red(sibling)) {
243 /* 218 /*
244 * Case 1 - le 219 * Case 1 - left rotate at parent
245 * 220 *
246 * P 221 * P S
247 * / \ 222 * / \ / \
248 * N s 223 * N s --> p Sr
249 * / \ 224 * / \ / \
250 * Sl Sr 225 * Sl Sr N Sl
251 */ 226 */
252 tmp1 = sibling !! 227 parent->rb_right = tmp1 = sibling->rb_left;
253 WRITE_ONCE(par !! 228 sibling->rb_left = parent;
254 WRITE_ONCE(sib <<
255 rb_set_parent_ 229 rb_set_parent_color(tmp1, parent, RB_BLACK);
256 __rb_rotate_se 230 __rb_rotate_set_parents(parent, sibling, root,
257 231 RB_RED);
258 augment_rotate 232 augment_rotate(parent, sibling);
259 sibling = tmp1 233 sibling = tmp1;
260 } 234 }
261 tmp1 = sibling->rb_rig 235 tmp1 = sibling->rb_right;
262 if (!tmp1 || rb_is_bla 236 if (!tmp1 || rb_is_black(tmp1)) {
263 tmp2 = sibling 237 tmp2 = sibling->rb_left;
264 if (!tmp2 || r 238 if (!tmp2 || rb_is_black(tmp2)) {
265 /* 239 /*
266 * Cas 240 * Case 2 - sibling color flip
267 * (p 241 * (p could be either color here)
268 * 242 *
269 * 243 * (p) (p)
270 * 244 * / \ / \
271 * N 245 * N S --> N s
272 * 246 * / \ / \
273 * 247 * Sl Sr Sl Sr
274 * 248 *
275 * Thi 249 * This leaves us violating 5) which
276 * can 250 * can be fixed by flipping p to black
277 * if 251 * if it was red, or by recursing at p.
278 * p i 252 * p is red when coming from Case 1.
279 */ 253 */
280 rb_set 254 rb_set_parent_color(sibling, parent,
281 255 RB_RED);
282 if (rb 256 if (rb_is_red(parent))
283 257 rb_set_black(parent);
284 else { 258 else {
285 259 node = parent;
286 260 parent = rb_parent(node);
287 261 if (parent)
288 262 continue;
289 } 263 }
290 break; 264 break;
291 } 265 }
292 /* 266 /*
293 * Case 3 - ri 267 * Case 3 - right rotate at sibling
294 * (p could be 268 * (p could be either color here)
295 * 269 *
296 * (p) 270 * (p) (p)
297 * / \ 271 * / \ / \
298 * N S - !! 272 * N S --> N Sl
299 * / \ 273 * / \ \
300 * sl sr !! 274 * sl Sr s
301 * 275 * \
302 * !! 276 * Sr
303 * <<
304 * Note: p mig <<
305 * p and sl ar <<
306 * breaks prop <<
307 * Case 4 (in <<
308 * whi <<
309 * and <<
310 * <<
311 * (p) <<
312 * / \ <<
313 * N sl - <<
314 * \ <<
315 * S <<
316 * \ <<
317 * sr <<
318 */ 277 */
319 tmp1 = tmp2->r !! 278 sibling->rb_left = tmp1 = tmp2->rb_right;
320 WRITE_ONCE(sib !! 279 tmp2->rb_right = sibling;
321 WRITE_ONCE(tmp !! 280 parent->rb_right = tmp2;
322 WRITE_ONCE(par <<
323 if (tmp1) 281 if (tmp1)
324 rb_set 282 rb_set_parent_color(tmp1, sibling,
325 283 RB_BLACK);
326 augment_rotate 284 augment_rotate(sibling, tmp2);
327 tmp1 = sibling 285 tmp1 = sibling;
328 sibling = tmp2 286 sibling = tmp2;
329 } 287 }
330 /* 288 /*
331 * Case 4 - left rotat 289 * Case 4 - left rotate at parent + color flips
332 * (p and sl could be 290 * (p and sl could be either color here.
333 * After rotation, p 291 * After rotation, p becomes black, s acquires
334 * p's color, and sl 292 * p's color, and sl keeps its color)
335 * 293 *
336 * (p) 294 * (p) (s)
337 * / \ 295 * / \ / \
338 * N S --> 296 * N S --> P Sr
339 * / \ 297 * / \ / \
340 * (sl) sr N 298 * (sl) sr N (sl)
341 */ 299 */
342 tmp2 = sibling->rb_lef !! 300 parent->rb_right = tmp2 = sibling->rb_left;
343 WRITE_ONCE(parent->rb_ !! 301 sibling->rb_left = parent;
344 WRITE_ONCE(sibling->rb <<
345 rb_set_parent_color(tm 302 rb_set_parent_color(tmp1, sibling, RB_BLACK);
346 if (tmp2) 303 if (tmp2)
347 rb_set_parent( 304 rb_set_parent(tmp2, parent);
348 __rb_rotate_set_parent 305 __rb_rotate_set_parents(parent, sibling, root,
349 306 RB_BLACK);
350 augment_rotate(parent, 307 augment_rotate(parent, sibling);
351 break; 308 break;
352 } else { 309 } else {
353 sibling = parent->rb_l 310 sibling = parent->rb_left;
354 if (rb_is_red(sibling) 311 if (rb_is_red(sibling)) {
355 /* Case 1 - ri 312 /* Case 1 - right rotate at parent */
356 tmp1 = sibling !! 313 parent->rb_left = tmp1 = sibling->rb_right;
357 WRITE_ONCE(par !! 314 sibling->rb_right = parent;
358 WRITE_ONCE(sib <<
359 rb_set_parent_ 315 rb_set_parent_color(tmp1, parent, RB_BLACK);
360 __rb_rotate_se 316 __rb_rotate_set_parents(parent, sibling, root,
361 317 RB_RED);
362 augment_rotate 318 augment_rotate(parent, sibling);
363 sibling = tmp1 319 sibling = tmp1;
364 } 320 }
365 tmp1 = sibling->rb_lef 321 tmp1 = sibling->rb_left;
366 if (!tmp1 || rb_is_bla 322 if (!tmp1 || rb_is_black(tmp1)) {
367 tmp2 = sibling 323 tmp2 = sibling->rb_right;
368 if (!tmp2 || r 324 if (!tmp2 || rb_is_black(tmp2)) {
369 /* Cas 325 /* Case 2 - sibling color flip */
370 rb_set 326 rb_set_parent_color(sibling, parent,
371 327 RB_RED);
372 if (rb 328 if (rb_is_red(parent))
373 329 rb_set_black(parent);
374 else { 330 else {
375 331 node = parent;
376 332 parent = rb_parent(node);
377 333 if (parent)
378 334 continue;
379 } 335 }
380 break; 336 break;
381 } 337 }
382 /* Case 3 - le !! 338 /* Case 3 - right rotate at sibling */
383 tmp1 = tmp2->r !! 339 sibling->rb_right = tmp1 = tmp2->rb_left;
384 WRITE_ONCE(sib !! 340 tmp2->rb_left = sibling;
385 WRITE_ONCE(tmp !! 341 parent->rb_left = tmp2;
386 WRITE_ONCE(par <<
387 if (tmp1) 342 if (tmp1)
388 rb_set 343 rb_set_parent_color(tmp1, sibling,
389 344 RB_BLACK);
390 augment_rotate 345 augment_rotate(sibling, tmp2);
391 tmp1 = sibling 346 tmp1 = sibling;
392 sibling = tmp2 347 sibling = tmp2;
393 } 348 }
394 /* Case 4 - right rota !! 349 /* Case 4 - left rotate at parent + color flips */
395 tmp2 = sibling->rb_rig !! 350 parent->rb_left = tmp2 = sibling->rb_right;
396 WRITE_ONCE(parent->rb_ !! 351 sibling->rb_right = parent;
397 WRITE_ONCE(sibling->rb <<
398 rb_set_parent_color(tm 352 rb_set_parent_color(tmp1, sibling, RB_BLACK);
399 if (tmp2) 353 if (tmp2)
400 rb_set_parent( 354 rb_set_parent(tmp2, parent);
401 __rb_rotate_set_parent 355 __rb_rotate_set_parents(parent, sibling, root,
402 356 RB_BLACK);
403 augment_rotate(parent, 357 augment_rotate(parent, sibling);
404 break; 358 break;
405 } 359 }
406 } 360 }
407 } 361 }
408 362
409 /* Non-inline version for rb_erase_augmented() 363 /* Non-inline version for rb_erase_augmented() use */
410 void __rb_erase_color(struct rb_node *parent, 364 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
411 void (*augment_rotate)(struct rb_node 365 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
412 { 366 {
413 ____rb_erase_color(parent, root, augme 367 ____rb_erase_color(parent, root, augment_rotate);
414 } 368 }
415 EXPORT_SYMBOL(__rb_erase_color); 369 EXPORT_SYMBOL(__rb_erase_color);
416 370
417 /* 371 /*
418 * Non-augmented rbtree manipulation functions 372 * Non-augmented rbtree manipulation functions.
419 * 373 *
420 * We use dummy augmented callbacks here, and 374 * We use dummy augmented callbacks here, and have the compiler optimize them
421 * out of the rb_insert_color() and rb_erase() 375 * out of the rb_insert_color() and rb_erase() function definitions.
422 */ 376 */
423 377
424 static inline void dummy_propagate(struct rb_n 378 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
425 static inline void dummy_copy(struct rb_node * 379 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
426 static inline void dummy_rotate(struct rb_node 380 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
427 381
428 static const struct rb_augment_callbacks dummy 382 static const struct rb_augment_callbacks dummy_callbacks = {
429 .propagate = dummy_propagate, !! 383 dummy_propagate, dummy_copy, dummy_rotate
430 .copy = dummy_copy, <<
431 .rotate = dummy_rotate <<
432 }; 384 };
433 385
434 void rb_insert_color(struct rb_node *node, str 386 void rb_insert_color(struct rb_node *node, struct rb_root *root)
435 { 387 {
436 __rb_insert(node, root, dummy_rotate); 388 __rb_insert(node, root, dummy_rotate);
437 } 389 }
438 EXPORT_SYMBOL(rb_insert_color); 390 EXPORT_SYMBOL(rb_insert_color);
439 391
440 void rb_erase(struct rb_node *node, struct rb_ 392 void rb_erase(struct rb_node *node, struct rb_root *root)
441 { 393 {
442 struct rb_node *rebalance; 394 struct rb_node *rebalance;
443 rebalance = __rb_erase_augmented(node, 395 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
444 if (rebalance) 396 if (rebalance)
445 ____rb_erase_color(rebalance, 397 ____rb_erase_color(rebalance, root, dummy_rotate);
446 } 398 }
447 EXPORT_SYMBOL(rb_erase); 399 EXPORT_SYMBOL(rb_erase);
448 400
449 /* 401 /*
450 * Augmented rbtree manipulation functions. 402 * Augmented rbtree manipulation functions.
451 * 403 *
452 * This instantiates the same __always_inline 404 * This instantiates the same __always_inline functions as in the non-augmented
453 * case, but this time with user-defined callb 405 * case, but this time with user-defined callbacks.
454 */ 406 */
455 407
456 void __rb_insert_augmented(struct rb_node *nod 408 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
457 void (*augment_rotate)(struct rb_node 409 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
458 { 410 {
459 __rb_insert(node, root, augment_rotate 411 __rb_insert(node, root, augment_rotate);
460 } 412 }
461 EXPORT_SYMBOL(__rb_insert_augmented); 413 EXPORT_SYMBOL(__rb_insert_augmented);
462 414
463 /* 415 /*
464 * This function returns the first node (in so 416 * This function returns the first node (in sort order) of the tree.
465 */ 417 */
466 struct rb_node *rb_first(const struct rb_root 418 struct rb_node *rb_first(const struct rb_root *root)
467 { 419 {
468 struct rb_node *n; 420 struct rb_node *n;
469 421
470 n = root->rb_node; 422 n = root->rb_node;
471 if (!n) 423 if (!n)
472 return NULL; 424 return NULL;
473 while (n->rb_left) 425 while (n->rb_left)
474 n = n->rb_left; 426 n = n->rb_left;
475 return n; 427 return n;
476 } 428 }
477 EXPORT_SYMBOL(rb_first); 429 EXPORT_SYMBOL(rb_first);
478 430
479 struct rb_node *rb_last(const struct rb_root * 431 struct rb_node *rb_last(const struct rb_root *root)
480 { 432 {
481 struct rb_node *n; 433 struct rb_node *n;
482 434
483 n = root->rb_node; 435 n = root->rb_node;
484 if (!n) 436 if (!n)
485 return NULL; 437 return NULL;
486 while (n->rb_right) 438 while (n->rb_right)
487 n = n->rb_right; 439 n = n->rb_right;
488 return n; 440 return n;
489 } 441 }
490 EXPORT_SYMBOL(rb_last); 442 EXPORT_SYMBOL(rb_last);
491 443
492 struct rb_node *rb_next(const struct rb_node * 444 struct rb_node *rb_next(const struct rb_node *node)
493 { 445 {
494 struct rb_node *parent; 446 struct rb_node *parent;
495 447
496 if (RB_EMPTY_NODE(node)) 448 if (RB_EMPTY_NODE(node))
497 return NULL; 449 return NULL;
498 450
499 /* 451 /*
500 * If we have a right-hand child, go d 452 * If we have a right-hand child, go down and then left as far
501 * as we can. 453 * as we can.
502 */ 454 */
503 if (node->rb_right) { 455 if (node->rb_right) {
504 node = node->rb_right; !! 456 node = node->rb_right;
505 while (node->rb_left) 457 while (node->rb_left)
506 node = node->rb_left; !! 458 node=node->rb_left;
507 return (struct rb_node *)node; 459 return (struct rb_node *)node;
508 } 460 }
509 461
510 /* 462 /*
511 * No right-hand children. Everything 463 * No right-hand children. Everything down and left is smaller than us,
512 * so any 'next' node must be in the g 464 * so any 'next' node must be in the general direction of our parent.
513 * Go up the tree; any time the ancest 465 * Go up the tree; any time the ancestor is a right-hand child of its
514 * parent, keep going up. First time i 466 * parent, keep going up. First time it's a left-hand child of its
515 * parent, said parent is our 'next' n 467 * parent, said parent is our 'next' node.
516 */ 468 */
517 while ((parent = rb_parent(node)) && n 469 while ((parent = rb_parent(node)) && node == parent->rb_right)
518 node = parent; 470 node = parent;
519 471
520 return parent; 472 return parent;
521 } 473 }
522 EXPORT_SYMBOL(rb_next); 474 EXPORT_SYMBOL(rb_next);
523 475
524 struct rb_node *rb_prev(const struct rb_node * 476 struct rb_node *rb_prev(const struct rb_node *node)
525 { 477 {
526 struct rb_node *parent; 478 struct rb_node *parent;
527 479
528 if (RB_EMPTY_NODE(node)) 480 if (RB_EMPTY_NODE(node))
529 return NULL; 481 return NULL;
530 482
531 /* 483 /*
532 * If we have a left-hand child, go do 484 * If we have a left-hand child, go down and then right as far
533 * as we can. 485 * as we can.
534 */ 486 */
535 if (node->rb_left) { 487 if (node->rb_left) {
536 node = node->rb_left; !! 488 node = node->rb_left;
537 while (node->rb_right) 489 while (node->rb_right)
538 node = node->rb_right; !! 490 node=node->rb_right;
539 return (struct rb_node *)node; 491 return (struct rb_node *)node;
540 } 492 }
541 493
542 /* 494 /*
543 * No left-hand children. Go up till w 495 * No left-hand children. Go up till we find an ancestor which
544 * is a right-hand child of its parent 496 * is a right-hand child of its parent.
545 */ 497 */
546 while ((parent = rb_parent(node)) && n 498 while ((parent = rb_parent(node)) && node == parent->rb_left)
547 node = parent; 499 node = parent;
548 500
549 return parent; 501 return parent;
550 } 502 }
551 EXPORT_SYMBOL(rb_prev); 503 EXPORT_SYMBOL(rb_prev);
552 504
553 void rb_replace_node(struct rb_node *victim, s 505 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
554 struct rb_root *root) 506 struct rb_root *root)
555 { 507 {
556 struct rb_node *parent = rb_parent(vic 508 struct rb_node *parent = rb_parent(victim);
557 509
558 /* Copy the pointers/colour from the v <<
559 *new = *victim; <<
560 <<
561 /* Set the surrounding nodes to point 510 /* Set the surrounding nodes to point to the replacement */
>> 511 __rb_change_child(victim, new, parent, root);
562 if (victim->rb_left) 512 if (victim->rb_left)
563 rb_set_parent(victim->rb_left, 513 rb_set_parent(victim->rb_left, new);
564 if (victim->rb_right) 514 if (victim->rb_right)
565 rb_set_parent(victim->rb_right 515 rb_set_parent(victim->rb_right, new);
566 __rb_change_child(victim, new, parent, <<
567 } <<
568 EXPORT_SYMBOL(rb_replace_node); <<
569 <<
570 void rb_replace_node_rcu(struct rb_node *victi <<
571 struct rb_root *root) <<
572 { <<
573 struct rb_node *parent = rb_parent(vic <<
574 516
575 /* Copy the pointers/colour from the v 517 /* Copy the pointers/colour from the victim to the replacement */
576 *new = *victim; 518 *new = *victim;
577 <<
578 /* Set the surrounding nodes to point <<
579 if (victim->rb_left) <<
580 rb_set_parent(victim->rb_left, <<
581 if (victim->rb_right) <<
582 rb_set_parent(victim->rb_right <<
583 <<
584 /* Set the parent's pointer to the new <<
585 * so that the pointers onwards are se <<
586 * an RCU walk over the tree. <<
587 */ <<
588 __rb_change_child_rcu(victim, new, par <<
589 } 519 }
590 EXPORT_SYMBOL(rb_replace_node_rcu); !! 520 EXPORT_SYMBOL(rb_replace_node);
591 <<
592 static struct rb_node *rb_left_deepest_node(co <<
593 { <<
594 for (;;) { <<
595 if (node->rb_left) <<
596 node = node->rb_left; <<
597 else if (node->rb_right) <<
598 node = node->rb_right; <<
599 else <<
600 return (struct rb_node <<
601 } <<
602 } <<
603 <<
604 struct rb_node *rb_next_postorder(const struct <<
605 { <<
606 const struct rb_node *parent; <<
607 if (!node) <<
608 return NULL; <<
609 parent = rb_parent(node); <<
610 <<
611 /* If we're sitting on node, we've alr <<
612 if (parent && node == parent->rb_left <<
613 /* If we are the parent's left <<
614 * node then all the way down <<
615 return rb_left_deepest_node(pa <<
616 } else <<
617 /* Otherwise we are the parent <<
618 * should be next */ <<
619 return (struct rb_node *)paren <<
620 } <<
621 EXPORT_SYMBOL(rb_next_postorder); <<
622 <<
623 struct rb_node *rb_first_postorder(const struc <<
624 { <<
625 if (!root->rb_node) <<
626 return NULL; <<
627 <<
628 return rb_left_deepest_node(root->rb_n <<
629 } <<
630 EXPORT_SYMBOL(rb_first_postorder); <<
631 521
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