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1// SPDX-License-Identifier: GPL-2.0-or-later2/*3 Red Black Trees4 (C) 1999 Andrea Arcangeli <andrea@suse.de>5 (C) 2002 David Woodhouse <dwmw2@infradead.org>6 (C) 2012 Michel Lespinasse <walken@google.com>7 8 9 linux/lib/rbtree.c10*/11 12#include <linux/rbtree_augmented.h>13#include <linux/export.h>14 15/*16 * red-black trees properties: https://en.wikipedia.org/wiki/Rbtree17 *18 * 1) A node is either red or black19 * 2) The root is black20 * 3) All leaves (NULL) are black21 * 4) Both children of every red node are black22 * 5) Every simple path from root to leaves contains the same number23 * of black nodes.24 *25 * 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two26 * consecutive red nodes in a path and every red node is therefore followed by27 * a black. So if B is the number of black nodes on every simple path (as per28 * 5), then the longest possible path due to 4 is 2B.29 *30 * We shall indicate color with case, where black nodes are uppercase and red31 * nodes will be lowercase. Unknown color nodes shall be drawn as red within32 * parentheses and have some accompanying text comment.33 */34 35/*36 * Notes on lockless lookups:37 *38 * All stores to the tree structure (rb_left and rb_right) must be done using39 * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the40 * tree structure as seen in program order.41 *42 * These two requirements will allow lockless iteration of the tree -- not43 * correct iteration mind you, tree rotations are not atomic so a lookup might44 * miss entire subtrees.45 *46 * But they do guarantee that any such traversal will only see valid elements47 * and that it will indeed complete -- does not get stuck in a loop.48 *49 * It also guarantees that if the lookup returns an element it is the 'correct'50 * one. But not returning an element does _NOT_ mean it's not present.51 *52 * NOTE:53 *54 * Stores to __rb_parent_color are not important for simple lookups so those55 * are left undone as of now. Nor did I check for loops involving parent56 * pointers.57 */58 59static inline void rb_set_black(struct rb_node *rb)60{61 rb->__rb_parent_color += RB_BLACK;62}63 64static inline struct rb_node *rb_red_parent(struct rb_node *red)65{66 return (struct rb_node *)red->__rb_parent_color;67}68 69/*70 * Helper function for rotations:71 * - old's parent and color get assigned to new72 * - old gets assigned new as a parent and 'color' as a color.73 */74static inline void75__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,76 struct rb_root *root, int color)77{78 struct rb_node *parent = rb_parent(old);79 new->__rb_parent_color = old->__rb_parent_color;80 rb_set_parent_color(old, new, color);81 __rb_change_child(old, new, parent, root);82}83 84static __always_inline void85__rb_insert(struct rb_node *node, struct rb_root *root,86 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))87{88 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;89 90 while (true) {91 /*92 * Loop invariant: node is red.93 */94 if (unlikely(!parent)) {95 /*96 * The inserted node is root. Either this is the97 * first node, or we recursed at Case 1 below and98 * are no longer violating 4).99 */100 rb_set_parent_color(node, NULL, RB_BLACK);101 break;102 }103 104 /*105 * If there is a black parent, we are done.106 * Otherwise, take some corrective action as,107 * per 4), we don't want a red root or two108 * consecutive red nodes.109 */110 if(rb_is_black(parent))111 break;112 113 gparent = rb_red_parent(parent);114 115 tmp = gparent->rb_right;116 if (parent != tmp) { /* parent == gparent->rb_left */117 if (tmp && rb_is_red(tmp)) {118 /*119 * Case 1 - node's uncle is red (color flips).120 *121 * G g122 * / \ / \123 * p u --> P U124 * / /125 * n n126 *127 * However, since g's parent might be red, and128 * 4) does not allow this, we need to recurse129 * at g.130 */131 rb_set_parent_color(tmp, gparent, RB_BLACK);132 rb_set_parent_color(parent, gparent, RB_BLACK);133 node = gparent;134 parent = rb_parent(node);135 rb_set_parent_color(node, parent, RB_RED);136 continue;137 }138 139 tmp = parent->rb_right;140 if (node == tmp) {141 /*142 * Case 2 - node's uncle is black and node is143 * the parent's right child (left rotate at parent).144 *145 * G G146 * / \ / \147 * p U --> n U148 * \ /149 * n p150 *151 * This still leaves us in violation of 4), the152 * continuation into Case 3 will fix that.153 */154 tmp = node->rb_left;155 WRITE_ONCE(parent->rb_right, tmp);156 WRITE_ONCE(node->rb_left, parent);157 if (tmp)158 rb_set_parent_color(tmp, parent,159 RB_BLACK);160 rb_set_parent_color(parent, node, RB_RED);161 augment_rotate(parent, node);162 parent = node;163 tmp = node->rb_right;164 }165 166 /*167 * Case 3 - node's uncle is black and node is168 * the parent's left child (right rotate at gparent).169 *170 * G P171 * / \ / \172 * p U --> n g173 * / \174 * n U175 */176 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */177 WRITE_ONCE(parent->rb_right, gparent);178 if (tmp)179 rb_set_parent_color(tmp, gparent, RB_BLACK);180 __rb_rotate_set_parents(gparent, parent, root, RB_RED);181 augment_rotate(gparent, parent);182 break;183 } else {184 tmp = gparent->rb_left;185 if (tmp && rb_is_red(tmp)) {186 /* Case 1 - color flips */187 rb_set_parent_color(tmp, gparent, RB_BLACK);188 rb_set_parent_color(parent, gparent, RB_BLACK);189 node = gparent;190 parent = rb_parent(node);191 rb_set_parent_color(node, parent, RB_RED);192 continue;193 }194 195 tmp = parent->rb_left;196 if (node == tmp) {197 /* Case 2 - right rotate at parent */198 tmp = node->rb_right;199 WRITE_ONCE(parent->rb_left, tmp);200 WRITE_ONCE(node->rb_right, parent);201 if (tmp)202 rb_set_parent_color(tmp, parent,203 RB_BLACK);204 rb_set_parent_color(parent, node, RB_RED);205 augment_rotate(parent, node);206 parent = node;207 tmp = node->rb_left;208 }209 210 /* Case 3 - left rotate at gparent */211 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */212 WRITE_ONCE(parent->rb_left, gparent);213 if (tmp)214 rb_set_parent_color(tmp, gparent, RB_BLACK);215 __rb_rotate_set_parents(gparent, parent, root, RB_RED);216 augment_rotate(gparent, parent);217 break;218 }219 }220}221 222/*223 * Inline version for rb_erase() use - we want to be able to inline224 * and eliminate the dummy_rotate callback there225 */226static __always_inline void227____rb_erase_color(struct rb_node *parent, struct rb_root *root,228 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))229{230 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;231 232 while (true) {233 /*234 * Loop invariants:235 * - node is black (or NULL on first iteration)236 * - node is not the root (parent is not NULL)237 * - All leaf paths going through parent and node have a238 * black node count that is 1 lower than other leaf paths.239 */240 sibling = parent->rb_right;241 if (node != sibling) { /* node == parent->rb_left */242 if (rb_is_red(sibling)) {243 /*244 * Case 1 - left rotate at parent245 *246 * P S247 * / \ / \248 * N s --> p Sr249 * / \ / \250 * Sl Sr N Sl251 */252 tmp1 = sibling->rb_left;253 WRITE_ONCE(parent->rb_right, tmp1);254 WRITE_ONCE(sibling->rb_left, parent);255 rb_set_parent_color(tmp1, parent, RB_BLACK);256 __rb_rotate_set_parents(parent, sibling, root,257 RB_RED);258 augment_rotate(parent, sibling);259 sibling = tmp1;260 }261 tmp1 = sibling->rb_right;262 if (!tmp1 || rb_is_black(tmp1)) {263 tmp2 = sibling->rb_left;264 if (!tmp2 || rb_is_black(tmp2)) {265 /*266 * Case 2 - sibling color flip267 * (p could be either color here)268 *269 * (p) (p)270 * / \ / \271 * N S --> N s272 * / \ / \273 * Sl Sr Sl Sr274 *275 * This leaves us violating 5) which276 * can be fixed by flipping p to black277 * if it was red, or by recursing at p.278 * p is red when coming from Case 1.279 */280 rb_set_parent_color(sibling, parent,281 RB_RED);282 if (rb_is_red(parent))283 rb_set_black(parent);284 else {285 node = parent;286 parent = rb_parent(node);287 if (parent)288 continue;289 }290 break;291 }292 /*293 * Case 3 - right rotate at sibling294 * (p could be either color here)295 *296 * (p) (p)297 * / \ / \298 * N S --> N sl299 * / \ \300 * sl Sr S301 * \302 * Sr303 *304 * Note: p might be red, and then both305 * p and sl are red after rotation(which306 * breaks property 4). This is fixed in307 * Case 4 (in __rb_rotate_set_parents()308 * which set sl the color of p309 * and set p RB_BLACK)310 *311 * (p) (sl)312 * / \ / \313 * N sl --> P S314 * \ / \315 * S N Sr316 * \317 * Sr318 */319 tmp1 = tmp2->rb_right;320 WRITE_ONCE(sibling->rb_left, tmp1);321 WRITE_ONCE(tmp2->rb_right, sibling);322 WRITE_ONCE(parent->rb_right, tmp2);323 if (tmp1)324 rb_set_parent_color(tmp1, sibling,325 RB_BLACK);326 augment_rotate(sibling, tmp2);327 tmp1 = sibling;328 sibling = tmp2;329 }330 /*331 * Case 4 - left rotate at parent + color flips332 * (p and sl could be either color here.333 * After rotation, p becomes black, s acquires334 * p's color, and sl keeps its color)335 *336 * (p) (s)337 * / \ / \338 * N S --> P Sr339 * / \ / \340 * (sl) sr N (sl)341 */342 tmp2 = sibling->rb_left;343 WRITE_ONCE(parent->rb_right, tmp2);344 WRITE_ONCE(sibling->rb_left, parent);345 rb_set_parent_color(tmp1, sibling, RB_BLACK);346 if (tmp2)347 rb_set_parent(tmp2, parent);348 __rb_rotate_set_parents(parent, sibling, root,349 RB_BLACK);350 augment_rotate(parent, sibling);351 break;352 } else {353 sibling = parent->rb_left;354 if (rb_is_red(sibling)) {355 /* Case 1 - right rotate at parent */356 tmp1 = sibling->rb_right;357 WRITE_ONCE(parent->rb_left, tmp1);358 WRITE_ONCE(sibling->rb_right, parent);359 rb_set_parent_color(tmp1, parent, RB_BLACK);360 __rb_rotate_set_parents(parent, sibling, root,361 RB_RED);362 augment_rotate(parent, sibling);363 sibling = tmp1;364 }365 tmp1 = sibling->rb_left;366 if (!tmp1 || rb_is_black(tmp1)) {367 tmp2 = sibling->rb_right;368 if (!tmp2 || rb_is_black(tmp2)) {369 /* Case 2 - sibling color flip */370 rb_set_parent_color(sibling, parent,371 RB_RED);372 if (rb_is_red(parent))373 rb_set_black(parent);374 else {375 node = parent;376 parent = rb_parent(node);377 if (parent)378 continue;379 }380 break;381 }382 /* Case 3 - left rotate at sibling */383 tmp1 = tmp2->rb_left;384 WRITE_ONCE(sibling->rb_right, tmp1);385 WRITE_ONCE(tmp2->rb_left, sibling);386 WRITE_ONCE(parent->rb_left, tmp2);387 if (tmp1)388 rb_set_parent_color(tmp1, sibling,389 RB_BLACK);390 augment_rotate(sibling, tmp2);391 tmp1 = sibling;392 sibling = tmp2;393 }394 /* Case 4 - right rotate at parent + color flips */395 tmp2 = sibling->rb_right;396 WRITE_ONCE(parent->rb_left, tmp2);397 WRITE_ONCE(sibling->rb_right, parent);398 rb_set_parent_color(tmp1, sibling, RB_BLACK);399 if (tmp2)400 rb_set_parent(tmp2, parent);401 __rb_rotate_set_parents(parent, sibling, root,402 RB_BLACK);403 augment_rotate(parent, sibling);404 break;405 }406 }407}408 409/* Non-inline version for rb_erase_augmented() use */410void __rb_erase_color(struct rb_node *parent, struct rb_root *root,411 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))412{413 ____rb_erase_color(parent, root, augment_rotate);414}415 416/*417 * Non-augmented rbtree manipulation functions.418 *419 * We use dummy augmented callbacks here, and have the compiler optimize them420 * out of the rb_insert_color() and rb_erase() function definitions.421 */422 423static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}424static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}425static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}426 427static const struct rb_augment_callbacks dummy_callbacks = {428 .propagate = dummy_propagate,429 .copy = dummy_copy,430 .rotate = dummy_rotate431};432 433void rb_insert_color(struct rb_node *node, struct rb_root *root)434{435 __rb_insert(node, root, dummy_rotate);436}437 438void rb_erase(struct rb_node *node, struct rb_root *root)439{440 struct rb_node *rebalance;441 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);442 if (rebalance)443 ____rb_erase_color(rebalance, root, dummy_rotate);444}445 446/*447 * Augmented rbtree manipulation functions.448 *449 * This instantiates the same __always_inline functions as in the non-augmented450 * case, but this time with user-defined callbacks.451 */452 453void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,454 void (*augment_rotate)(struct rb_node *old, struct rb_node *new))455{456 __rb_insert(node, root, augment_rotate);457}458 459/*460 * This function returns the first node (in sort order) of the tree.461 */462struct rb_node *rb_first(const struct rb_root *root)463{464 struct rb_node *n;465 466 n = root->rb_node;467 if (!n)468 return NULL;469 while (n->rb_left)470 n = n->rb_left;471 return n;472}473 474struct rb_node *rb_last(const struct rb_root *root)475{476 struct rb_node *n;477 478 n = root->rb_node;479 if (!n)480 return NULL;481 while (n->rb_right)482 n = n->rb_right;483 return n;484}485 486struct rb_node *rb_next(const struct rb_node *node)487{488 struct rb_node *parent;489 490 if (RB_EMPTY_NODE(node))491 return NULL;492 493 /*494 * If we have a right-hand child, go down and then left as far495 * as we can.496 */497 if (node->rb_right) {498 node = node->rb_right;499 while (node->rb_left)500 node = node->rb_left;501 return (struct rb_node *)node;502 }503 504 /*505 * No right-hand children. Everything down and left is smaller than us,506 * so any 'next' node must be in the general direction of our parent.507 * Go up the tree; any time the ancestor is a right-hand child of its508 * parent, keep going up. First time it's a left-hand child of its509 * parent, said parent is our 'next' node.510 */511 while ((parent = rb_parent(node)) && node == parent->rb_right)512 node = parent;513 514 return parent;515}516 517struct rb_node *rb_prev(const struct rb_node *node)518{519 struct rb_node *parent;520 521 if (RB_EMPTY_NODE(node))522 return NULL;523 524 /*525 * If we have a left-hand child, go down and then right as far526 * as we can.527 */528 if (node->rb_left) {529 node = node->rb_left;530 while (node->rb_right)531 node = node->rb_right;532 return (struct rb_node *)node;533 }534 535 /*536 * No left-hand children. Go up till we find an ancestor which537 * is a right-hand child of its parent.538 */539 while ((parent = rb_parent(node)) && node == parent->rb_left)540 node = parent;541 542 return parent;543}544 545void rb_replace_node(struct rb_node *victim, struct rb_node *new,546 struct rb_root *root)547{548 struct rb_node *parent = rb_parent(victim);549 550 /* Copy the pointers/colour from the victim to the replacement */551 *new = *victim;552 553 /* Set the surrounding nodes to point to the replacement */554 if (victim->rb_left)555 rb_set_parent(victim->rb_left, new);556 if (victim->rb_right)557 rb_set_parent(victim->rb_right, new);558 __rb_change_child(victim, new, parent, root);559}560 561static struct rb_node *rb_left_deepest_node(const struct rb_node *node)562{563 for (;;) {564 if (node->rb_left)565 node = node->rb_left;566 else if (node->rb_right)567 node = node->rb_right;568 else569 return (struct rb_node *)node;570 }571}572 573struct rb_node *rb_next_postorder(const struct rb_node *node)574{575 const struct rb_node *parent;576 if (!node)577 return NULL;578 parent = rb_parent(node);579 580 /* If we're sitting on node, we've already seen our children */581 if (parent && node == parent->rb_left && parent->rb_right) {582 /* If we are the parent's left node, go to the parent's right583 * node then all the way down to the left */584 return rb_left_deepest_node(parent->rb_right);585 } else586 /* Otherwise we are the parent's right node, and the parent587 * should be next */588 return (struct rb_node *)parent;589}590 591struct rb_node *rb_first_postorder(const struct rb_root *root)592{593 if (!root->rb_node)594 return NULL;595 596 return rb_left_deepest_node(root->rb_node);597}598