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 dummy_propagate, dummy_copy, dummy_rotate 431 }; 432 433 void rb_insert_color(struct rb_node *node, struct rb_root *root) 434 { 435 __rb_insert(node, root, dummy_rotate); 436 } 437 EXPORT_SYMBOL(rb_insert_color); 438 439 void rb_erase(struct rb_node *node, struct rb_root *root) 440 { 441 struct rb_node *rebalance; 442 rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); 443 if (rebalance) 444 ____rb_erase_color(rebalance, root, dummy_rotate); 445 } 446 EXPORT_SYMBOL(rb_erase); 447 448 /* 449 * Augmented rbtree manipulation functions. 450 * 451 * This instantiates the same __always_inline functions as in the non-augmented 452 * case, but this time with user-defined callbacks. 453 */ 454 455 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, 456 void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) 457 { 458 __rb_insert(node, root, augment_rotate); 459 } 460 EXPORT_SYMBOL(__rb_insert_augmented); 461 462 /* 463 * This function returns the first node (in sort order) of the tree. 464 */ 465 struct rb_node *rb_first(const struct rb_root *root) 466 { 467 struct rb_node *n; 468 469 n = root->rb_node; 470 if (!n) 471 return NULL; 472 while (n->rb_left) 473 n = n->rb_left; 474 return n; 475 } 476 EXPORT_SYMBOL(rb_first); 477 478 struct rb_node *rb_last(const struct rb_root *root) 479 { 480 struct rb_node *n; 481 482 n = root->rb_node; 483 if (!n) 484 return NULL; 485 while (n->rb_right) 486 n = n->rb_right; 487 return n; 488 } 489 EXPORT_SYMBOL(rb_last); 490 491 struct rb_node *rb_next(const struct rb_node *node) 492 { 493 struct rb_node *parent; 494 495 if (RB_EMPTY_NODE(node)) 496 return NULL; 497 498 /* 499 * If we have a right-hand child, go down and then left as far 500 * as we can. 501 */ 502 if (node->rb_right) { 503 node = node->rb_right; 504 while (node->rb_left) 505 node=node->rb_left; 506 return (struct rb_node *)node; 507 } 508 509 /* 510 * No right-hand children. Everything down and left is smaller than us, 511 * so any 'next' node must be in the general direction of our parent. 512 * Go up the tree; any time the ancestor is a right-hand child of its 513 * parent, keep going up. First time it's a left-hand child of its 514 * parent, said parent is our 'next' node. 515 */ 516 while ((parent = rb_parent(node)) && node == parent->rb_right) 517 node = parent; 518 519 return parent; 520 } 521 EXPORT_SYMBOL(rb_next); 522 523 struct rb_node *rb_prev(const struct rb_node *node) 524 { 525 struct rb_node *parent; 526 527 if (RB_EMPTY_NODE(node)) 528 return NULL; 529 530 /* 531 * If we have a left-hand child, go down and then right as far 532 * as we can. 533 */ 534 if (node->rb_left) { 535 node = node->rb_left; 536 while (node->rb_right) 537 node=node->rb_right; 538 return (struct rb_node *)node; 539 } 540 541 /* 542 * No left-hand children. Go up till we find an ancestor which 543 * is a right-hand child of its parent. 544 */ 545 while ((parent = rb_parent(node)) && node == parent->rb_left) 546 node = parent; 547 548 return parent; 549 } 550 EXPORT_SYMBOL(rb_prev); 551 552 void rb_replace_node(struct rb_node *victim, struct rb_node *new, 553 struct rb_root *root) 554 { 555 struct rb_node *parent = rb_parent(victim); 556 557 /* Copy the pointers/colour from the victim to the replacement */ 558 *new = *victim; 559 560 /* Set the surrounding nodes to point to the replacement */ 561 if (victim->rb_left) 562 rb_set_parent(victim->rb_left, new); 563 if (victim->rb_right) 564 rb_set_parent(victim->rb_right, new); 565 __rb_change_child(victim, new, parent, root); 566 } 567 EXPORT_SYMBOL(rb_replace_node); 568 569 void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new, 570 struct rb_root *root) 571 { 572 struct rb_node *parent = rb_parent(victim); 573 574 /* Copy the pointers/colour from the victim to the replacement */ 575 *new = *victim; 576 577 /* Set the surrounding nodes to point to the replacement */ 578 if (victim->rb_left) 579 rb_set_parent(victim->rb_left, new); 580 if (victim->rb_right) 581 rb_set_parent(victim->rb_right, new); 582 583 /* Set the parent's pointer to the new node last after an RCU barrier 584 * so that the pointers onwards are seen to be set correctly when doing 585 * an RCU walk over the tree. 586 */ 587 __rb_change_child_rcu(victim, new, parent, root); 588 } 589 EXPORT_SYMBOL(rb_replace_node_rcu); 590 591 static struct rb_node *rb_left_deepest_node(const struct rb_node *node) 592 { 593 for (;;) { 594 if (node->rb_left) 595 node = node->rb_left; 596 else if (node->rb_right) 597 node = node->rb_right; 598 else 599 return (struct rb_node *)node; 600 } 601 } 602 603 struct rb_node *rb_next_postorder(const struct rb_node *node) 604 { 605 const struct rb_node *parent; 606 if (!node) 607 return NULL; 608 parent = rb_parent(node); 609 610 /* If we're sitting on node, we've already seen our children */ 611 if (parent && node == parent->rb_left && parent->rb_right) { 612 /* If we are the parent's left node, go to the parent's right 613 * node then all the way down to the left */ 614 return rb_left_deepest_node(parent->rb_right); 615 } else 616 /* Otherwise we are the parent's right node, and the parent 617 * should be next */ 618 return (struct rb_node *)parent; 619 } 620 EXPORT_SYMBOL(rb_next_postorder); 621 622 struct rb_node *rb_first_postorder(const struct rb_root *root) 623 { 624 if (!root->rb_node) 625 return NULL; 626 627 return rb_left_deepest_node(root->rb_node); 628 } 629 EXPORT_SYMBOL(rb_first_postorder); 630