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ARM: mm: use bitmap operations when allocating new ASIDs
[linux-2.6.git] / lib / rbtree.c
blob4f56a11d67fa9da105b34337280277d6fe437b2e
1 /*
2 Red Black Trees
3 (C) 1999 Andrea Arcangeli <andrea@suse.de>
4 (C) 2002 David Woodhouse <dwmw2@infradead.org>
5 (C) 2012 Michel Lespinasse <walken@google.com>
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
20
21 linux/lib/rbtree.c
22 */
23
24 #include <linux/rbtree_augmented.h>
25 #include <linux/export.h>
26
27 /*
28 * red-black trees properties: http://en.wikipedia.org/wiki/Rbtree
29 *
30 * 1) A node is either red or black
31 * 2) The root is black
32 * 3) All leaves (NULL) are black
33 * 4) Both children of every red node are black
34 * 5) Every simple path from root to leaves contains the same number
35 * of black nodes.
36 *
37 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
38 * consecutive red nodes in a path and every red node is therefore followed by
39 * a black. So if B is the number of black nodes on every simple path (as per
40 * 5), then the longest possible path due to 4 is 2B.
41 *
42 * We shall indicate color with case, where black nodes are uppercase and red
43 * nodes will be lowercase. Unknown color nodes shall be drawn as red within
44 * parentheses and have some accompanying text comment.
45 */
46
47 static inline void rb_set_black(struct rb_node *rb)
48 {
49 rb->__rb_parent_color |= RB_BLACK;
50 }
51
52 static inline struct rb_node *rb_red_parent(struct rb_node *red)
53 {
54 return (struct rb_node *)red->__rb_parent_color;
55 }
56
57 /*
58 * Helper function for rotations:
59 * - old's parent and color get assigned to new
60 * - old gets assigned new as a parent and 'color' as a color.
61 */
62 static inline void
63 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
64 struct rb_root *root, int color)
65 {
66 struct rb_node *parent = rb_parent(old);
67 new->__rb_parent_color = old->__rb_parent_color;
68 rb_set_parent_color(old, new, color);
69 __rb_change_child(old, new, parent, root);
70 }
71
72 static __always_inline void
73 __rb_insert(struct rb_node *node, struct rb_root *root,
74 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
75 {
76 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
77
78 while (true) {
79 /*
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.
85 */
86 if (!parent) {
87 rb_set_parent_color(node, NULL, RB_BLACK);
88 break;
89 } else if (rb_is_black(parent))
90 break;
91
92 gparent = rb_red_parent(parent);
93
94 tmp = gparent->rb_right;
95 if (parent != tmp) { /* parent == gparent->rb_left */
96 if (tmp && rb_is_red(tmp)) {
97 /*
98 * Case 1 - color flips
99 *
100 * G g
101 * / \ / \
102 * p u --> P U
103 * / /
104 * n N
105 *
106 * However, since g's parent might be red, and
107 * 4) does not allow this, we need to recurse
108 * at g.
109 */
110 rb_set_parent_color(tmp, gparent, RB_BLACK);
111 rb_set_parent_color(parent, gparent, RB_BLACK);
112 node = gparent;
113 parent = rb_parent(node);
114 rb_set_parent_color(node, parent, RB_RED);
115 continue;
116 }
117
118 tmp = parent->rb_right;
119 if (node == tmp) {
120 /*
121 * Case 2 - left rotate at parent
122 *
123 * G G
124 * / \ / \
125 * p U --> n U
126 * \ /
127 * n p
128 *
129 * This still leaves us in violation of 4), the
130 * continuation into Case 3 will fix that.
131 */
132 parent->rb_right = tmp = node->rb_left;
133 node->rb_left = parent;
134 if (tmp)
135 rb_set_parent_color(tmp, parent,
136 RB_BLACK);
137 rb_set_parent_color(parent, node, RB_RED);
138 augment_rotate(parent, node);
139 parent = node;
140 tmp = node->rb_right;
141 }
142
143 /*
144 * Case 3 - right rotate at gparent
145 *
146 * G P
147 * / \ / \
148 * p U --> n g
149 * / \
150 * n U
151 */
152 gparent->rb_left = tmp; /* == parent->rb_right */
153 parent->rb_right = gparent;
154 if (tmp)
155 rb_set_parent_color(tmp, gparent, RB_BLACK);
156 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
157 augment_rotate(gparent, parent);
158 break;
159 } else {
160 tmp = gparent->rb_left;
161 if (tmp && rb_is_red(tmp)) {
162 /* Case 1 - color flips */
163 rb_set_parent_color(tmp, gparent, RB_BLACK);
164 rb_set_parent_color(parent, gparent, RB_BLACK);
165 node = gparent;
166 parent = rb_parent(node);
167 rb_set_parent_color(node, parent, RB_RED);
168 continue;
169 }
170
171 tmp = parent->rb_left;
172 if (node == tmp) {
173 /* Case 2 - right rotate at parent */
174 parent->rb_left = tmp = node->rb_right;
175 node->rb_right = parent;
176 if (tmp)
177 rb_set_parent_color(tmp, parent,
178 RB_BLACK);
179 rb_set_parent_color(parent, node, RB_RED);
180 augment_rotate(parent, node);
181 parent = node;
182 tmp = node->rb_left;
183 }
184
185 /* Case 3 - left rotate at gparent */
186 gparent->rb_right = tmp; /* == parent->rb_left */
187 parent->rb_left = gparent;
188 if (tmp)
189 rb_set_parent_color(tmp, gparent, RB_BLACK);
190 __rb_rotate_set_parents(gparent, parent, root, RB_RED);
191 augment_rotate(gparent, parent);
192 break;
193 }
194 }
195 }
196
197 __always_inline void
198 __rb_erase_color(struct rb_node *parent, struct rb_root *root,
199 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
200 {
201 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
202
203 while (true) {
204 /*
205 * Loop invariants:
206 * - node is black (or NULL on first iteration)
207 * - node is not the root (parent is not NULL)
208 * - All leaf paths going through parent and node have a
209 * black node count that is 1 lower than other leaf paths.
210 */
211 sibling = parent->rb_right;
212 if (node != sibling) { /* node == parent->rb_left */
213 if (rb_is_red(sibling)) {
214 /*
215 * Case 1 - left rotate at parent
216 *
217 * P S
218 * / \ / \
219 * N s --> p Sr
220 * / \ / \
221 * Sl Sr N Sl
222 */
223 parent->rb_right = tmp1 = sibling->rb_left;
224 sibling->rb_left = parent;
225 rb_set_parent_color(tmp1, parent, RB_BLACK);
226 __rb_rotate_set_parents(parent, sibling, root,
227 RB_RED);
228 augment_rotate(parent, sibling);
229 sibling = tmp1;
230 }
231 tmp1 = sibling->rb_right;
232 if (!tmp1 || rb_is_black(tmp1)) {
233 tmp2 = sibling->rb_left;
234 if (!tmp2 || rb_is_black(tmp2)) {
235 /*
236 * Case 2 - sibling color flip
237 * (p could be either color here)
238 *
239 * (p) (p)
240 * / \ / \
241 * N S --> N s
242 * / \ / \
243 * Sl Sr Sl Sr
244 *
245 * This leaves us violating 5) which
246 * can be fixed by flipping p to black
247 * if it was red, or by recursing at p.
248 * p is red when coming from Case 1.
249 */
250 rb_set_parent_color(sibling, parent,
251 RB_RED);
252 if (rb_is_red(parent))
253 rb_set_black(parent);
254 else {
255 node = parent;
256 parent = rb_parent(node);
257 if (parent)
258 continue;
259 }
260 break;
261 }
262 /*
263 * Case 3 - right rotate at sibling
264 * (p could be either color here)
265 *
266 * (p) (p)
267 * / \ / \
268 * N S --> N Sl
269 * / \ \
270 * sl Sr s
271 * \
272 * Sr
273 */
274 sibling->rb_left = tmp1 = tmp2->rb_right;
275 tmp2->rb_right = sibling;
276 parent->rb_right = tmp2;
277 if (tmp1)
278 rb_set_parent_color(tmp1, sibling,
279 RB_BLACK);
280 augment_rotate(sibling, tmp2);
281 tmp1 = sibling;
282 sibling = tmp2;
283 }
284 /*
285 * Case 4 - left rotate at parent + color flips
286 * (p and sl could be either color here.
287 * After rotation, p becomes black, s acquires
288 * p's color, and sl keeps its color)
289 *
290 * (p) (s)
291 * / \ / \
292 * N S --> P Sr
293 * / \ / \
294 * (sl) sr N (sl)
295 */
296 parent->rb_right = tmp2 = sibling->rb_left;
297 sibling->rb_left = parent;
298 rb_set_parent_color(tmp1, sibling, RB_BLACK);
299 if (tmp2)
300 rb_set_parent(tmp2, parent);
301 __rb_rotate_set_parents(parent, sibling, root,
302 RB_BLACK);
303 augment_rotate(parent, sibling);
304 break;
305 } else {
306 sibling = parent->rb_left;
307 if (rb_is_red(sibling)) {
308 /* Case 1 - right rotate at parent */
309 parent->rb_left = tmp1 = sibling->rb_right;
310 sibling->rb_right = parent;
311 rb_set_parent_color(tmp1, parent, RB_BLACK);
312 __rb_rotate_set_parents(parent, sibling, root,
313 RB_RED);
314 augment_rotate(parent, sibling);
315 sibling = tmp1;
316 }
317 tmp1 = sibling->rb_left;
318 if (!tmp1 || rb_is_black(tmp1)) {
319 tmp2 = sibling->rb_right;
320 if (!tmp2 || rb_is_black(tmp2)) {
321 /* Case 2 - sibling color flip */
322 rb_set_parent_color(sibling, parent,
323 RB_RED);
324 if (rb_is_red(parent))
325 rb_set_black(parent);
326 else {
327 node = parent;
328 parent = rb_parent(node);
329 if (parent)
330 continue;
331 }
332 break;
333 }
334 /* Case 3 - right rotate at sibling */
335 sibling->rb_right = tmp1 = tmp2->rb_left;
336 tmp2->rb_left = sibling;
337 parent->rb_left = tmp2;
338 if (tmp1)
339 rb_set_parent_color(tmp1, sibling,
340 RB_BLACK);
341 augment_rotate(sibling, tmp2);
342 tmp1 = sibling;
343 sibling = tmp2;
344 }
345 /* Case 4 - left rotate at parent + color flips */
346 parent->rb_left = tmp2 = sibling->rb_right;
347 sibling->rb_right = parent;
348 rb_set_parent_color(tmp1, sibling, RB_BLACK);
349 if (tmp2)
350 rb_set_parent(tmp2, parent);
351 __rb_rotate_set_parents(parent, sibling, root,
352 RB_BLACK);
353 augment_rotate(parent, sibling);
354 break;
355 }
356 }
357 }
358 EXPORT_SYMBOL(__rb_erase_color);
359
360 /*
361 * Non-augmented rbtree manipulation functions.
362 *
363 * We use dummy augmented callbacks here, and have the compiler optimize them
364 * out of the rb_insert_color() and rb_erase() function definitions.
365 */
366
367 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
368 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
369 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
370
371 static const struct rb_augment_callbacks dummy_callbacks = {
372 dummy_propagate, dummy_copy, dummy_rotate
373 };
374
375 void rb_insert_color(struct rb_node *node, struct rb_root *root)
376 {
377 __rb_insert(node, root, dummy_rotate);
378 }
379 EXPORT_SYMBOL(rb_insert_color);
380
381 void rb_erase(struct rb_node *node, struct rb_root *root)
382 {
383 rb_erase_augmented(node, root, &dummy_callbacks);
384 }
385 EXPORT_SYMBOL(rb_erase);
386
387 /*
388 * Augmented rbtree manipulation functions.
389 *
390 * This instantiates the same __always_inline functions as in the non-augmented
391 * case, but this time with user-defined callbacks.
392 */
393
394 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
395 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
396 {
397 __rb_insert(node, root, augment_rotate);
398 }
399 EXPORT_SYMBOL(__rb_insert_augmented);
400
401 /*
402 * This function returns the first node (in sort order) of the tree.
403 */
404 struct rb_node *rb_first(const struct rb_root *root)
405 {
406 struct rb_node *n;
407
408 n = root->rb_node;
409 if (!n)
410 return NULL;
411 while (n->rb_left)
412 n = n->rb_left;
413 return n;
414 }
415 EXPORT_SYMBOL(rb_first);
416
417 struct rb_node *rb_last(const struct rb_root *root)
418 {
419 struct rb_node *n;
420
421 n = root->rb_node;
422 if (!n)
423 return NULL;
424 while (n->rb_right)
425 n = n->rb_right;
426 return n;
427 }
428 EXPORT_SYMBOL(rb_last);
429
430 struct rb_node *rb_next(const struct rb_node *node)
431 {
432 struct rb_node *parent;
433
434 if (RB_EMPTY_NODE(node))
435 return NULL;
436
437 /*
438 * If we have a right-hand child, go down and then left as far
439 * as we can.
440 */
441 if (node->rb_right) {
442 node = node->rb_right;
443 while (node->rb_left)
444 node=node->rb_left;
445 return (struct rb_node *)node;
446 }
447
448 /*
449 * No right-hand children. Everything down and left is smaller than us,
450 * so any 'next' node must be in the general direction of our parent.
451 * Go up the tree; any time the ancestor is a right-hand child of its
452 * parent, keep going up. First time it's a left-hand child of its
453 * parent, said parent is our 'next' node.
454 */
455 while ((parent = rb_parent(node)) && node == parent->rb_right)
456 node = parent;
457
458 return parent;
459 }
460 EXPORT_SYMBOL(rb_next);
461
462 struct rb_node *rb_prev(const struct rb_node *node)
463 {
464 struct rb_node *parent;
465
466 if (RB_EMPTY_NODE(node))
467 return NULL;
468
469 /*
470 * If we have a left-hand child, go down and then right as far
471 * as we can.
472 */
473 if (node->rb_left) {
474 node = node->rb_left;
475 while (node->rb_right)
476 node=node->rb_right;
477 return (struct rb_node *)node;
478 }
479
480 /*
481 * No left-hand children. Go up till we find an ancestor which
482 * is a right-hand child of its parent.
483 */
484 while ((parent = rb_parent(node)) && node == parent->rb_left)
485 node = parent;
486
487 return parent;
488 }
489 EXPORT_SYMBOL(rb_prev);
490
491 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
492 struct rb_root *root)
493 {
494 struct rb_node *parent = rb_parent(victim);
495
496 /* Set the surrounding nodes to point to the replacement */
497 __rb_change_child(victim, new, parent, root);
498 if (victim->rb_left)
499 rb_set_parent(victim->rb_left, new);
500 if (victim->rb_right)
501 rb_set_parent(victim->rb_right, new);
502
503 /* Copy the pointers/colour from the victim to the replacement */
504 *new = *victim;
505 }
506 EXPORT_SYMBOL(rb_replace_node);
Linus' kernel tree