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 /* 48 * Notes on lockless lookups: 49 * 50 * All stores to the tree structure (rb_left and rb_right) must be done using 51 * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the 52 * tree structure as seen in program order. 53 * 54 * These two requirements will allow lockless iteration of the tree -- not 55 * correct iteration mind you, tree rotations are not atomic so a lookup might 56 * miss entire subtrees. 57 * 58 * But they do guarantee that any such traversal will only see valid elements 59 * and that it will indeed complete -- does not get stuck in a loop. 60 * 61 * It also guarantees that if the lookup returns an element it is the 'correct' 62 * one. But not returning an element does _NOT_ mean it's not present. 63 * 64 * NOTE: 65 * 66 * Stores to __rb_parent_color are not important for simple lookups so those 67 * are left undone as of now. Nor did I check for loops involving parent 68 * pointers. 69 */ 70 71 static inline void rb_set_black(struct rb_node *rb) 72 { 73 rb->__rb_parent_color |= RB_BLACK; 74 } 75 76 static inline struct rb_node *rb_red_parent(struct rb_node *red) 77 { 78 return (struct rb_node *)red->__rb_parent_color; 79 } 80 81 /* 82 * Helper function for rotations: 83 * - old's parent and color get assigned to new 84 * - old gets assigned new as a parent and 'color' as a color. 85 */ 86 static inline void 87 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, 88 struct rb_root *root, int color) 89 { 90 struct rb_node *parent = rb_parent(old); 91 new->__rb_parent_color = old->__rb_parent_color; 92 rb_set_parent_color(old, new, color); 93 __rb_change_child(old, new, parent, root); 94 } 95 96 static __always_inline void 97 __rb_insert(struct rb_node *node, struct rb_root *root, 98 bool newleft, struct rb_node **leftmost, 99 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 100 { 101 struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; 102 103 if (newleft) 104 *leftmost = node; 105 106 while (true) { 107 /* 108 * Loop invariant: node is red. 109 */ 110 if (unlikely(!parent)) { 111 /* 112 * The inserted node is root. Either this is the 113 * first node, or we recursed at Case 1 below and 114 * are no longer violating 4). 115 */ 116 rb_set_parent_color(node, NULL, RB_BLACK); 117 break; 118 } 119 120 /* 121 * If there is a black parent, we are done. 122 * Otherwise, take some corrective action as, 123 * per 4), we don't want a red root or two 124 * consecutive red nodes. 125 */ 126 if(rb_is_black(parent)) 127 break; 128 129 gparent = rb_red_parent(parent); 130 131 tmp = gparent->rb_right; 132 if (parent != tmp) { /* parent == gparent->rb_left */ 133 if (tmp && rb_is_red(tmp)) { 134 /* 135 * Case 1 - node's uncle is red (color flips). 136 * 137 * G g 138 * / \ / \ 139 * p u --> P U 140 * / / 141 * n n 142 * 143 * However, since g's parent might be red, and 144 * 4) does not allow this, we need to recurse 145 * at g. 146 */ 147 rb_set_parent_color(tmp, gparent, RB_BLACK); 148 rb_set_parent_color(parent, gparent, RB_BLACK); 149 node = gparent; 150 parent = rb_parent(node); 151 rb_set_parent_color(node, parent, RB_RED); 152 continue; 153 } 154 155 tmp = parent->rb_right; 156 if (node == tmp) { 157 /* 158 * Case 2 - node's uncle is black and node is 159 * the parent's right child (left rotate at parent). 160 * 161 * G G 162 * / \ / \ 163 * p U --> n U 164 * \ / 165 * n p 166 * 167 * This still leaves us in violation of 4), the 168 * continuation into Case 3 will fix that. 169 */ 170 tmp = node->rb_left; 171 WRITE_ONCE(parent->rb_right, tmp); 172 WRITE_ONCE(node->rb_left, parent); 173 if (tmp) 174 rb_set_parent_color(tmp, parent, 175 RB_BLACK); 176 rb_set_parent_color(parent, node, RB_RED); 177 augment_rotate(parent, node); 178 parent = node; 179 tmp = node->rb_right; 180 } 181 182 /* 183 * Case 3 - node's uncle is black and node is 184 * the parent's left child (right rotate at gparent). 185 * 186 * G P 187 * / \ / \ 188 * p U --> n g 189 * / \ 190 * n U 191 */ 192 WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */ 193 WRITE_ONCE(parent->rb_right, gparent); 194 if (tmp) 195 rb_set_parent_color(tmp, gparent, RB_BLACK); 196 __rb_rotate_set_parents(gparent, parent, root, RB_RED); 197 augment_rotate(gparent, parent); 198 break; 199 } else { 200 tmp = gparent->rb_left; 201 if (tmp && rb_is_red(tmp)) { 202 /* Case 1 - color flips */ 203 rb_set_parent_color(tmp, gparent, RB_BLACK); 204 rb_set_parent_color(parent, gparent, RB_BLACK); 205 node = gparent; 206 parent = rb_parent(node); 207 rb_set_parent_color(node, parent, RB_RED); 208 continue; 209 } 210 211 tmp = parent->rb_left; 212 if (node == tmp) { 213 /* Case 2 - right rotate at parent */ 214 tmp = node->rb_right; 215 WRITE_ONCE(parent->rb_left, tmp); 216 WRITE_ONCE(node->rb_right, parent); 217 if (tmp) 218 rb_set_parent_color(tmp, parent, 219 RB_BLACK); 220 rb_set_parent_color(parent, node, RB_RED); 221 augment_rotate(parent, node); 222 parent = node; 223 tmp = node->rb_left; 224 } 225 226 /* Case 3 - left rotate at gparent */ 227 WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */ 228 WRITE_ONCE(parent->rb_left, gparent); 229 if (tmp) 230 rb_set_parent_color(tmp, gparent, RB_BLACK); 231 __rb_rotate_set_parents(gparent, parent, root, RB_RED); 232 augment_rotate(gparent, parent); 233 break; 234 } 235 } 236 } 237 238 /* 239 * Inline version for rb_erase() use - we want to be able to inline 240 * and eliminate the dummy_rotate callback there 241 */ 242 static __always_inline void 243 ____rb_erase_color(struct rb_node *parent, struct rb_root *root, 244 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 245 { 246 struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; 247 248 while (true) { 249 /* 250 * Loop invariants: 251 * - node is black (or NULL on first iteration) 252 * - node is not the root (parent is not NULL) 253 * - All leaf paths going through parent and node have a 254 * black node count that is 1 lower than other leaf paths. 255 */ 256 sibling = parent->rb_right; 257 if (node != sibling) { /* node == parent->rb_left */ 258 if (rb_is_red(sibling)) { 259 /* 260 * Case 1 - left rotate at parent 261 * 262 * P S 263 * / \ / \ 264 * N s --> p Sr 265 * / \ / \ 266 * Sl Sr N Sl 267 */ 268 tmp1 = sibling->rb_left; 269 WRITE_ONCE(parent->rb_right, tmp1); 270 WRITE_ONCE(sibling->rb_left, parent); 271 rb_set_parent_color(tmp1, parent, RB_BLACK); 272 __rb_rotate_set_parents(parent, sibling, root, 273 RB_RED); 274 augment_rotate(parent, sibling); 275 sibling = tmp1; 276 } 277 tmp1 = sibling->rb_right; 278 if (!tmp1 || rb_is_black(tmp1)) { 279 tmp2 = sibling->rb_left; 280 if (!tmp2 || rb_is_black(tmp2)) { 281 /* 282 * Case 2 - sibling color flip 283 * (p could be either color here) 284 * 285 * (p) (p) 286 * / \ / \ 287 * N S --> N s 288 * / \ / \ 289 * Sl Sr Sl Sr 290 * 291 * This leaves us violating 5) which 292 * can be fixed by flipping p to black 293 * if it was red, or by recursing at p. 294 * p is red when coming from Case 1. 295 */ 296 rb_set_parent_color(sibling, parent, 297 RB_RED); 298 if (rb_is_red(parent)) 299 rb_set_black(parent); 300 else { 301 node = parent; 302 parent = rb_parent(node); 303 if (parent) 304 continue; 305 } 306 break; 307 } 308 /* 309 * Case 3 - right rotate at sibling 310 * (p could be either color here) 311 * 312 * (p) (p) 313 * / \ / \ 314 * N S --> N sl 315 * / \ \ 316 * sl Sr S 317 * \ 318 * Sr 319 * 320 * Note: p might be red, and then both 321 * p and sl are red after rotation(which 322 * breaks property 4). This is fixed in 323 * Case 4 (in __rb_rotate_set_parents() 324 * which set sl the color of p 325 * and set p RB_BLACK) 326 * 327 * (p) (sl) 328 * / \ / \ 329 * N sl --> P S 330 * \ / \ 331 * S N Sr 332 * \ 333 * Sr 334 */ 335 tmp1 = tmp2->rb_right; 336 WRITE_ONCE(sibling->rb_left, tmp1); 337 WRITE_ONCE(tmp2->rb_right, sibling); 338 WRITE_ONCE(parent->rb_right, tmp2); 339 if (tmp1) 340 rb_set_parent_color(tmp1, sibling, 341 RB_BLACK); 342 augment_rotate(sibling, tmp2); 343 tmp1 = sibling; 344 sibling = tmp2; 345 } 346 /* 347 * Case 4 - left rotate at parent + color flips 348 * (p and sl could be either color here. 349 * After rotation, p becomes black, s acquires 350 * p's color, and sl keeps its color) 351 * 352 * (p) (s) 353 * / \ / \ 354 * N S --> P Sr 355 * / \ / \ 356 * (sl) sr N (sl) 357 */ 358 tmp2 = sibling->rb_left; 359 WRITE_ONCE(parent->rb_right, tmp2); 360 WRITE_ONCE(sibling->rb_left, parent); 361 rb_set_parent_color(tmp1, sibling, RB_BLACK); 362 if (tmp2) 363 rb_set_parent(tmp2, parent); 364 __rb_rotate_set_parents(parent, sibling, root, 365 RB_BLACK); 366 augment_rotate(parent, sibling); 367 break; 368 } else { 369 sibling = parent->rb_left; 370 if (rb_is_red(sibling)) { 371 /* Case 1 - right rotate at parent */ 372 tmp1 = sibling->rb_right; 373 WRITE_ONCE(parent->rb_left, tmp1); 374 WRITE_ONCE(sibling->rb_right, parent); 375 rb_set_parent_color(tmp1, parent, RB_BLACK); 376 __rb_rotate_set_parents(parent, sibling, root, 377 RB_RED); 378 augment_rotate(parent, sibling); 379 sibling = tmp1; 380 } 381 tmp1 = sibling->rb_left; 382 if (!tmp1 || rb_is_black(tmp1)) { 383 tmp2 = sibling->rb_right; 384 if (!tmp2 || rb_is_black(tmp2)) { 385 /* Case 2 - sibling color flip */ 386 rb_set_parent_color(sibling, parent, 387 RB_RED); 388 if (rb_is_red(parent)) 389 rb_set_black(parent); 390 else { 391 node = parent; 392 parent = rb_parent(node); 393 if (parent) 394 continue; 395 } 396 break; 397 } 398 /* Case 3 - left rotate at sibling */ 399 tmp1 = tmp2->rb_left; 400 WRITE_ONCE(sibling->rb_right, tmp1); 401 WRITE_ONCE(tmp2->rb_left, sibling); 402 WRITE_ONCE(parent->rb_left, tmp2); 403 if (tmp1) 404 rb_set_parent_color(tmp1, sibling, 405 RB_BLACK); 406 augment_rotate(sibling, tmp2); 407 tmp1 = sibling; 408 sibling = tmp2; 409 } 410 /* Case 4 - right rotate at parent + color flips */ 411 tmp2 = sibling->rb_right; 412 WRITE_ONCE(parent->rb_left, tmp2); 413 WRITE_ONCE(sibling->rb_right, parent); 414 rb_set_parent_color(tmp1, sibling, RB_BLACK); 415 if (tmp2) 416 rb_set_parent(tmp2, parent); 417 __rb_rotate_set_parents(parent, sibling, root, 418 RB_BLACK); 419 augment_rotate(parent, sibling); 420 break; 421 } 422 } 423 } 424 425 /* Non-inline version for rb_erase_augmented() use */ 426 void __rb_erase_color(struct rb_node *parent, struct rb_root *root, 427 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 428 { 429 ____rb_erase_color(parent, root, augment_rotate); 430 } 431 EXPORT_SYMBOL(__rb_erase_color); 432 433 /* 434 * Non-augmented rbtree manipulation functions. 435 * 436 * We use dummy augmented callbacks here, and have the compiler optimize them 437 * out of the rb_insert_color() and rb_erase() function definitions. 438 */ 439 440 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} 441 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} 442 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} 443 444 static const struct rb_augment_callbacks dummy_callbacks = { 445 .propagate = dummy_propagate, 446 .copy = dummy_copy, 447 .rotate = dummy_rotate 448 }; 449 450 void rb_insert_color(struct rb_node *node, struct rb_root *root) 451 { 452 __rb_insert(node, root, false, NULL, dummy_rotate); 453 } 454 EXPORT_SYMBOL(rb_insert_color); 455 456 void rb_erase(struct rb_node *node, struct rb_root *root) 457 { 458 struct rb_node *rebalance; 459 rebalance = __rb_erase_augmented(node, root, 460 NULL, &dummy_callbacks); 461 if (rebalance) 462 ____rb_erase_color(rebalance, root, dummy_rotate); 463 } 464 EXPORT_SYMBOL(rb_erase); 465 466 void rb_insert_color_cached(struct rb_node *node, 467 struct rb_root_cached *root, bool leftmost) 468 { 469 __rb_insert(node, &root->rb_root, leftmost, 470 &root->rb_leftmost, dummy_rotate); 471 } 472 EXPORT_SYMBOL(rb_insert_color_cached); 473 474 void rb_erase_cached(struct rb_node *node, struct rb_root_cached *root) 475 { 476 struct rb_node *rebalance; 477 rebalance = __rb_erase_augmented(node, &root->rb_root, 478 &root->rb_leftmost, &dummy_callbacks); 479 if (rebalance) 480 ____rb_erase_color(rebalance, &root->rb_root, dummy_rotate); 481 } 482 EXPORT_SYMBOL(rb_erase_cached); 483 484 /* 485 * Augmented rbtree manipulation functions. 486 * 487 * This instantiates the same __always_inline functions as in the non-augmented 488 * case, but this time with user-defined callbacks. 489 */ 490 491 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, 492 bool newleft, struct rb_node **leftmost, 493 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 494 { 495 __rb_insert(node, root, newleft, leftmost, augment_rotate); 496 } 497 EXPORT_SYMBOL(__rb_insert_augmented); 498 499 /* 500 * This function returns the first node (in sort order) of the tree. 501 */ 502 struct rb_node *rb_first(const struct rb_root *root) 503 { 504 struct rb_node *n; 505 506 n = root->rb_node; 507 if (!n) 508 return NULL; 509 while (n->rb_left) 510 n = n->rb_left; 511 return n; 512 } 513 EXPORT_SYMBOL(rb_first); 514 515 struct rb_node *rb_last(const struct rb_root *root) 516 { 517 struct rb_node *n; 518 519 n = root->rb_node; 520 if (!n) 521 return NULL; 522 while (n->rb_right) 523 n = n->rb_right; 524 return n; 525 } 526 EXPORT_SYMBOL(rb_last); 527 528 struct rb_node *rb_next(const struct rb_node *node) 529 { 530 struct rb_node *parent; 531 532 if (RB_EMPTY_NODE(node)) 533 return NULL; 534 535 /* 536 * If we have a right-hand child, go down and then left as far 537 * as we can. 538 */ 539 if (node->rb_right) { 540 node = node->rb_right; 541 while (node->rb_left) 542 node=node->rb_left; 543 return (struct rb_node *)node; 544 } 545 546 /* 547 * No right-hand children. Everything down and left is smaller than us, 548 * so any 'next' node must be in the general direction of our parent. 549 * Go up the tree; any time the ancestor is a right-hand child of its 550 * parent, keep going up. First time it's a left-hand child of its 551 * parent, said parent is our 'next' node. 552 */ 553 while ((parent = rb_parent(node)) && node == parent->rb_right) 554 node = parent; 555 556 return parent; 557 } 558 EXPORT_SYMBOL(rb_next); 559 560 struct rb_node *rb_prev(const struct rb_node *node) 561 { 562 struct rb_node *parent; 563 564 if (RB_EMPTY_NODE(node)) 565 return NULL; 566 567 /* 568 * If we have a left-hand child, go down and then right as far 569 * as we can. 570 */ 571 if (node->rb_left) { 572 node = node->rb_left; 573 while (node->rb_right) 574 node=node->rb_right; 575 return (struct rb_node *)node; 576 } 577 578 /* 579 * No left-hand children. Go up till we find an ancestor which 580 * is a right-hand child of its parent. 581 */ 582 while ((parent = rb_parent(node)) && node == parent->rb_left) 583 node = parent; 584 585 return parent; 586 } 587 EXPORT_SYMBOL(rb_prev); 588 589 void rb_replace_node(struct rb_node *victim, struct rb_node *new, 590 struct rb_root *root) 591 { 592 struct rb_node *parent = rb_parent(victim); 593 594 /* Copy the pointers/colour from the victim to the replacement */ 595 *new = *victim; 596 597 /* Set the surrounding nodes to point to the replacement */ 598 if (victim->rb_left) 599 rb_set_parent(victim->rb_left, new); 600 if (victim->rb_right) 601 rb_set_parent(victim->rb_right, new); 602 __rb_change_child(victim, new, parent, root); 603 } 604 EXPORT_SYMBOL(rb_replace_node); 605 606 void rb_replace_node_cached(struct rb_node *victim, struct rb_node *new, 607 struct rb_root_cached *root) 608 { 609 rb_replace_node(victim, new, &root->rb_root); 610 611 if (root->rb_leftmost == victim) 612 root->rb_leftmost = new; 613 } 614 EXPORT_SYMBOL(rb_replace_node_cached); 615 616 void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new, 617 struct rb_root *root) 618 { 619 struct rb_node *parent = rb_parent(victim); 620 621 /* Copy the pointers/colour from the victim to the replacement */ 622 *new = *victim; 623 624 /* Set the surrounding nodes to point to the replacement */ 625 if (victim->rb_left) 626 rb_set_parent(victim->rb_left, new); 627 if (victim->rb_right) 628 rb_set_parent(victim->rb_right, new); 629 630 /* Set the parent's pointer to the new node last after an RCU barrier 631 * so that the pointers onwards are seen to be set correctly when doing 632 * an RCU walk over the tree. 633 */ 634 __rb_change_child_rcu(victim, new, parent, root); 635 } 636 EXPORT_SYMBOL(rb_replace_node_rcu); 637 638 static struct rb_node *rb_left_deepest_node(const struct rb_node *node) 639 { 640 for (;;) { 641 if (node->rb_left) 642 node = node->rb_left; 643 else if (node->rb_right) 644 node = node->rb_right; 645 else 646 return (struct rb_node *)node; 647 } 648 } 649 650 struct rb_node *rb_next_postorder(const struct rb_node *node) 651 { 652 const struct rb_node *parent; 653 if (!node) 654 return NULL; 655 parent = rb_parent(node); 656 657 /* If we're sitting on node, we've already seen our children */ 658 if (parent && node == parent->rb_left && parent->rb_right) { 659 /* If we are the parent's left node, go to the parent's right 660 * node then all the way down to the left */ 661 return rb_left_deepest_node(parent->rb_right); 662 } else 663 /* Otherwise we are the parent's right node, and the parent 664 * should be next */ 665 return (struct rb_node *)parent; 666 } 667 EXPORT_SYMBOL(rb_next_postorder); 668 669 struct rb_node *rb_first_postorder(const struct rb_root *root) 670 { 671 if (!root->rb_node) 672 return NULL; 673 674 return rb_left_deepest_node(root->rb_node); 675 } 676 EXPORT_SYMBOL(rb_first_postorder); 677