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