lib/rbtree.c

   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);