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