kernel/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 #include <linux/rcupdate.h>
  27
  28 /*
  29  * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
  30  *
  31  *  1) A node is either red or black
  32  *  2) The root is black
  33  *  3) All leaves (NULL) are black
  34  *  4) Both children of every red node are black
  35  *  5) Every simple path from root to leaves contains the same number
  36  *     of black nodes.
  37  *
  38  *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
  39  *  consecutive red nodes in a path and every red node is therefore followed by
  40  *  a black. So if B is the number of black nodes on every simple path (as per
  41  *  5), then the longest possible path due to 4 is 2B.
  42  *
  43  *  We shall indicate color with case, where black nodes are uppercase and red
  44  *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
  45  *  parentheses and have some accompanying text comment.
  46  */
  47
  48 /*
  49  * Notes on lockless lookups:
  50  *
  51  * All stores to the tree structure (rb_left and rb_right) must be done using
  52  * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
  53  * tree structure as seen in program order.
  54  *
  55  * These two requirements will allow lockless iteration of the tree -- not
  56  * correct iteration mind you, tree rotations are not atomic so a lookup might
  57  * miss entire subtrees.
  58  *
  59  * But they do guarantee that any such traversal will only see valid elements
  60  * and that it will indeed complete -- does not get stuck in a loop.
  61  *
  62  * It also guarantees that if the lookup returns an element it is the 'correct'
  63  * one. But not returning an element does _NOT_ mean it's not present.
  64  *
  65  * NOTE:
  66  *
  67  * Stores to __rb_parent_color are not important for simple lookups so those
  68  * are left undone as of now. Nor did I check for loops involving parent
  69  * pointers.
  70  */
  71
  72 static inline void rb_set_black(struct rb_node *rb)
  73 {
  74         rb->__rb_parent_color |= RB_BLACK;
  75 }
  76
  77 static inline struct rb_node *rb_red_parent(struct rb_node *red)
  78 {
  79         return (struct rb_node *)red->__rb_parent_color;
  80 }
  81
  82 /*
  83  * Helper function for rotations:
  84  * - old's parent and color get assigned to new
  85  * - old gets assigned new as a parent and 'color' as a color.
  86  */
  87 static inline void
  88 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
  89                         struct rb_root *root, int color)
  90 {
  91         struct rb_node *parent = rb_parent(old);
  92         new->__rb_parent_color = old->__rb_parent_color;
  93         rb_set_parent_color(old, new, color);
  94         __rb_change_child(old, new, parent, root);
  95 }
  96
  97 static __always_inline void
  98 __rb_insert(struct rb_node *node, struct rb_root *root,
  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         while (true) {
 104                 /*
 105                  * Loop invariant: node is red
 106                  *
 107                  * If there is a black parent, we are done.
 108                  * Otherwise, take some corrective action as we don't
 109                  * want a red root or two consecutive red nodes.
 110                  */
 111                 if (!parent) {
 112                         rb_set_parent_color(node, NULL, RB_BLACK);
 113                         break;
 114                 } else if (rb_is_black(parent))
 115                         break;
 116
 117                 gparent = rb_red_parent(parent);
 118
 119                 tmp = gparent->rb_right;
 120                 if (parent != tmp) {    /* parent == gparent->rb_left */
 121                         if (tmp && rb_is_red(tmp)) {
 122                                 /*
 123                                  * Case 1 - color flips
 124                                  *
 125                                  *       G            g
 126                                  *      / \          / \
 127                                  *     p   u  -->   P   U
 128                                  *    /            /
 129                                  *   n            n
 130                                  *
 131                                  * However, since g's parent might be red, and
 132                                  * 4) does not allow this, we need to recurse
 133                                  * at g.
 134                                  */
 135                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 136                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 137                                 node = gparent;
 138                                 parent = rb_parent(node);
 139                                 rb_set_parent_color(node, parent, RB_RED);
 140                                 continue;
 141                         }
 142
 143                         tmp = parent->rb_right;
 144                         if (node == tmp) {
 145                                 /*
 146                                  * Case 2 - left rotate at parent
 147                                  *
 148                                  *      G             G
 149                                  *     / \           / \
 150                                  *    p   U  -->    n   U
 151                                  *     \           /
 152                                  *      n         p
 153                                  *
 154                                  * This still leaves us in violation of 4), the
 155                                  * continuation into Case 3 will fix that.
 156                                  */
 157                                 tmp = node->rb_left;
 158                                 WRITE_ONCE(parent->rb_right, tmp);
 159                                 WRITE_ONCE(node->rb_left, parent);
 160                                 if (tmp)
 161                                         rb_set_parent_color(tmp, parent,
 162                                                             RB_BLACK);
 163                                 rb_set_parent_color(parent, node, RB_RED);
 164                                 augment_rotate(parent, node);
 165                                 parent = node;
 166                                 tmp = node->rb_right;
 167                         }
 168
 169                         /*
 170                          * Case 3 - right rotate at gparent
 171                          *
 172                          *        G           P
 173                          *       / \         / \
 174                          *      p   U  -->  n   g
 175                          *     /                 \
 176                          *    n                   U
 177                          */
 178                         WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
 179                         WRITE_ONCE(parent->rb_right, gparent);
 180                         if (tmp)
 181                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 182                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 183                         augment_rotate(gparent, parent);
 184                         break;
 185                 } else {
 186                         tmp = gparent->rb_left;
 187                         if (tmp && rb_is_red(tmp)) {
 188                                 /* Case 1 - color flips */
 189                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 190                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 191                                 node = gparent;
 192                                 parent = rb_parent(node);
 193                                 rb_set_parent_color(node, parent, RB_RED);
 194                                 continue;
 195                         }
 196
 197                         tmp = parent->rb_left;
 198                         if (node == tmp) {
 199                                 /* Case 2 - right rotate at parent */
 200                                 tmp = node->rb_right;
 201                                 WRITE_ONCE(parent->rb_left, tmp);
 202                                 WRITE_ONCE(node->rb_right, parent);
 203                                 if (tmp)
 204                                         rb_set_parent_color(tmp, parent,
 205                                                             RB_BLACK);
 206                                 rb_set_parent_color(parent, node, RB_RED);
 207                                 augment_rotate(parent, node);
 208                                 parent = node;
 209                                 tmp = node->rb_left;
 210                         }
 211
 212                         /* Case 3 - left rotate at gparent */
 213                         WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
 214                         WRITE_ONCE(parent->rb_left, gparent);
 215                         if (tmp)
 216                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 217                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 218                         augment_rotate(gparent, parent);
 219                         break;
 220                 }
 221         }
 222 }
 223
 224 /*
 225  * Inline version for rb_erase() use - we want to be able to inline
 226  * and eliminate the dummy_rotate callback there
 227  */
 228 static __always_inline void
 229 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
 230         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 231 {
 232         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
 233
 234         while (true) {
 235                 /*
 236                  * Loop invariants:
 237                  * - node is black (or NULL on first iteration)
 238                  * - node is not the root (parent is not NULL)
 239                  * - All leaf paths going through parent and node have a
 240                  *   black node count that is 1 lower than other leaf paths.
 241                  */
 242                 sibling = parent->rb_right;
 243                 if (node != sibling) {  /* node == parent->rb_left */
 244                         if (rb_is_red(sibling)) {
 245                                 /*
 246                                  * Case 1 - left rotate at parent
 247                                  *
 248                                  *     P               S
 249                                  *    / \             / \
 250                                  *   N   s    -->    p   Sr
 251                                  *      / \         / \
 252                                  *     Sl  Sr      N   Sl
 253                                  */
 254                                 tmp1 = sibling->rb_left;
 255                                 WRITE_ONCE(parent->rb_right, tmp1);
 256                                 WRITE_ONCE(sibling->rb_left, parent);
 257                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 258                                 __rb_rotate_set_parents(parent, sibling, root,
 259                                                         RB_RED);
 260                                 augment_rotate(parent, sibling);
 261                                 sibling = tmp1;
 262                         }
 263                         tmp1 = sibling->rb_right;
 264                         if (!tmp1 || rb_is_black(tmp1)) {
 265                                 tmp2 = sibling->rb_left;
 266                                 if (!tmp2 || rb_is_black(tmp2)) {
 267                                         /*
 268                                          * Case 2 - sibling color flip
 269                                          * (p could be either color here)
 270                                          *
 271                                          *    (p)           (p)
 272                                          *    / \           / \
 273                                          *   N   S    -->  N   s
 274                                          *      / \           / \
 275                                          *     Sl  Sr        Sl  Sr
 276                                          *
 277                                          * This leaves us violating 5) which
 278                                          * can be fixed by flipping p to black
 279                                          * if it was red, or by recursing at p.
 280                                          * p is red when coming from Case 1.
 281                                          */
 282                                         rb_set_parent_color(sibling, parent,
 283                                                             RB_RED);
 284                                         if (rb_is_red(parent))
 285                                                 rb_set_black(parent);
 286                                         else {
 287                                                 node = parent;
 288                                                 parent = rb_parent(node);
 289                                                 if (parent)
 290                                                         continue;
 291                                         }
 292                                         break;
 293                                 }
 294                                 /*
 295                                  * Case 3 - right rotate at sibling
 296                                  * (p could be either color here)
 297                                  *
 298                                  *   (p)           (p)
 299                                  *   / \           / \
 300                                  *  N   S    -->  N   Sl
 301                                  *     / \             \
 302                                  *    sl  Sr            s
 303                                  *                       \
 304                                  *                        Sr
 305                                  */
 306                                 tmp1 = tmp2->rb_right;
 307                                 WRITE_ONCE(sibling->rb_left, tmp1);
 308                                 WRITE_ONCE(tmp2->rb_right, sibling);
 309                                 WRITE_ONCE(parent->rb_right, tmp2);
 310                                 if (tmp1)
 311                                         rb_set_parent_color(tmp1, sibling,
 312                                                             RB_BLACK);
 313                                 augment_rotate(sibling, tmp2);
 314                                 tmp1 = sibling;
 315                                 sibling = tmp2;
 316                         }
 317                         /*
 318                          * Case 4 - left rotate at parent + color flips
 319                          * (p and sl could be either color here.
 320                          *  After rotation, p becomes black, s acquires
 321                          *  p's color, and sl keeps its color)
 322                          *
 323                          *      (p)             (s)
 324                          *      / \             / \
 325                          *     N   S     -->   P   Sr
 326                          *        / \         / \
 327                          *      (sl) sr      N  (sl)
 328                          */
 329                         tmp2 = sibling->rb_left;
 330                         WRITE_ONCE(parent->rb_right, tmp2);
 331                         WRITE_ONCE(sibling->rb_left, parent);
 332                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 333                         if (tmp2)
 334                                 rb_set_parent(tmp2, parent);
 335                         __rb_rotate_set_parents(parent, sibling, root,
 336                                                 RB_BLACK);
 337                         augment_rotate(parent, sibling);
 338                         break;
 339                 } else {
 340                         sibling = parent->rb_left;
 341                         if (rb_is_red(sibling)) {
 342                                 /* Case 1 - right rotate at parent */
 343                                 tmp1 = sibling->rb_right;
 344                                 WRITE_ONCE(parent->rb_left, tmp1);
 345                                 WRITE_ONCE(sibling->rb_right, parent);
 346                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 347                                 __rb_rotate_set_parents(parent, sibling, root,
 348                                                         RB_RED);
 349                                 augment_rotate(parent, sibling);
 350                                 sibling = tmp1;
 351                         }
 352                         tmp1 = sibling->rb_left;
 353                         if (!tmp1 || rb_is_black(tmp1)) {
 354                                 tmp2 = sibling->rb_right;
 355                                 if (!tmp2 || rb_is_black(tmp2)) {
 356                                         /* Case 2 - sibling color flip */
 357                                         rb_set_parent_color(sibling, parent,
 358                                                             RB_RED);
 359                                         if (rb_is_red(parent))
 360                                                 rb_set_black(parent);
 361                                         else {
 362                                                 node = parent;
 363                                                 parent = rb_parent(node);
 364                                                 if (parent)
 365                                                         continue;
 366                                         }
 367                                         break;
 368                                 }
 369                                 /* Case 3 - right rotate at sibling */
 370                                 tmp1 = tmp2->rb_left;
 371                                 WRITE_ONCE(sibling->rb_right, tmp1);
 372                                 WRITE_ONCE(tmp2->rb_left, sibling);
 373                                 WRITE_ONCE(parent->rb_left, tmp2);
 374                                 if (tmp1)
 375                                         rb_set_parent_color(tmp1, sibling,
 376                                                             RB_BLACK);
 377                                 augment_rotate(sibling, tmp2);
 378                                 tmp1 = sibling;
 379                                 sibling = tmp2;
 380                         }
 381                         /* Case 4 - left rotate at parent + color flips */
 382                         tmp2 = sibling->rb_right;
 383                         WRITE_ONCE(parent->rb_left, tmp2);
 384                         WRITE_ONCE(sibling->rb_right, parent);
 385                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 386                         if (tmp2)
 387                                 rb_set_parent(tmp2, parent);
 388                         __rb_rotate_set_parents(parent, sibling, root,
 389                                                 RB_BLACK);
 390                         augment_rotate(parent, sibling);
 391                         break;
 392                 }
 393         }
 394 }
 395
 396 /* Non-inline version for rb_erase_augmented() use */
 397 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
 398         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 399 {
 400         ____rb_erase_color(parent, root, augment_rotate);
 401 }
 402 EXPORT_SYMBOL(__rb_erase_color);
 403
 404 /*
 405  * Non-augmented rbtree manipulation functions.
 406  *
 407  * We use dummy augmented callbacks here, and have the compiler optimize them
 408  * out of the rb_insert_color() and rb_erase() function definitions.
 409  */
 410
 411 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
 412 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
 413 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
 414
 415 static const struct rb_augment_callbacks dummy_callbacks = {
 416         dummy_propagate, dummy_copy, dummy_rotate
 417 };
 418
 419 void rb_insert_color(struct rb_node *node, struct rb_root *root)
 420 {
 421         __rb_insert(node, root, dummy_rotate);
 422 }
 423 EXPORT_SYMBOL(rb_insert_color);
 424
 425 void rb_erase(struct rb_node *node, struct rb_root *root)
 426 {
 427         struct rb_node *rebalance;
 428         rebalance = __rb_erase_augmented(node, root, &dummy_callbacks);
 429         if (rebalance)
 430                 ____rb_erase_color(rebalance, root, dummy_rotate);
 431 }
 432 EXPORT_SYMBOL(rb_erase);
 433
 434 /*
 435  * Augmented rbtree manipulation functions.
 436  *
 437  * This instantiates the same __always_inline functions as in the non-augmented
 438  * case, but this time with user-defined callbacks.
 439  */
 440
 441 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
 442         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 443 {
 444         __rb_insert(node, root, augment_rotate);
 445 }
 446 EXPORT_SYMBOL(__rb_insert_augmented);
 447
 448 /*
 449  * This function returns the first node (in sort order) of the tree.
 450  */
 451 struct rb_node *rb_first(const struct rb_root *root)
 452 {
 453         struct rb_node  *n;
 454
 455         n = root->rb_node;
 456         if (!n)
 457                 return NULL;
 458         while (n->rb_left)
 459                 n = n->rb_left;
 460         return n;
 461 }
 462 EXPORT_SYMBOL(rb_first);
 463
 464 struct rb_node *rb_last(const struct rb_root *root)
 465 {
 466         struct rb_node  *n;
 467
 468         n = root->rb_node;
 469         if (!n)
 470                 return NULL;
 471         while (n->rb_right)
 472                 n = n->rb_right;
 473         return n;
 474 }
 475 EXPORT_SYMBOL(rb_last);
 476
 477 struct rb_node *rb_next(const struct rb_node *node)
 478 {
 479         struct rb_node *parent;
 480
 481         if (RB_EMPTY_NODE(node))
 482                 return NULL;
 483
 484         /*
 485          * If we have a right-hand child, go down and then left as far
 486          * as we can.
 487          */
 488         if (node->rb_right) {
 489                 node = node->rb_right;
 490                 while (node->rb_left)
 491                         node=node->rb_left;
 492                 return (struct rb_node *)node;
 493         }
 494
 495         /*
 496          * No right-hand children. Everything down and left is smaller than us,
 497          * so any 'next' node must be in the general direction of our parent.
 498          * Go up the tree; any time the ancestor is a right-hand child of its
 499          * parent, keep going up. First time it's a left-hand child of its
 500          * parent, said parent is our 'next' node.
 501          */
 502         while ((parent = rb_parent(node)) && node == parent->rb_right)
 503                 node = parent;
 504
 505         return parent;
 506 }
 507 EXPORT_SYMBOL(rb_next);
 508
 509 struct rb_node *rb_prev(const struct rb_node *node)
 510 {
 511         struct rb_node *parent;
 512
 513         if (RB_EMPTY_NODE(node))
 514                 return NULL;
 515
 516         /*
 517          * If we have a left-hand child, go down and then right as far
 518          * as we can.
 519          */
 520         if (node->rb_left) {
 521                 node = node->rb_left;
 522                 while (node->rb_right)
 523                         node=node->rb_right;
 524                 return (struct rb_node *)node;
 525         }
 526
 527         /*
 528          * No left-hand children. Go up till we find an ancestor which
 529          * is a right-hand child of its parent.
 530          */
 531         while ((parent = rb_parent(node)) && node == parent->rb_left)
 532                 node = parent;
 533
 534         return parent;
 535 }
 536 EXPORT_SYMBOL(rb_prev);
 537
 538 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
 539                      struct rb_root *root)
 540 {
 541         struct rb_node *parent = rb_parent(victim);
 542
 543         /* Set the surrounding nodes to point to the replacement */
 544         __rb_change_child(victim, new, parent, root);
 545         if (victim->rb_left)
 546                 rb_set_parent(victim->rb_left, new);
 547         if (victim->rb_right)
 548                 rb_set_parent(victim->rb_right, new);
 549
 550         /* Copy the pointers/colour from the victim to the replacement */
 551         *new = *victim;
 552 }
 553 EXPORT_SYMBOL(rb_replace_node);
 554
 555 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
 556 {
 557         for (;;) {
 558                 if (node->rb_left)
 559                         node = node->rb_left;
 560                 else if (node->rb_right)
 561                         node = node->rb_right;
 562                 else
 563                         return (struct rb_node *)node;
 564         }
 565 }
 566
 567 struct rb_node *rb_next_postorder(const struct rb_node *node)
 568 {
 569         const struct rb_node *parent;
 570         if (!node)
 571                 return NULL;
 572         parent = rb_parent(node);
 573
 574         /* If we're sitting on node, we've already seen our children */
 575         if (parent && node == parent->rb_left && parent->rb_right) {
 576                 /* If we are the parent's left node, go to the parent's right
 577                  * node then all the way down to the left */
 578                 return rb_left_deepest_node(parent->rb_right);
 579         } else
 580                 /* Otherwise we are the parent's right node, and the parent
 581                  * should be next */
 582                 return (struct rb_node *)parent;
 583 }
 584 EXPORT_SYMBOL(rb_next_postorder);
 585
 586 struct rb_node *rb_first_postorder(const struct rb_root *root)
 587 {
 588         if (!root->rb_node)
 589                 return NULL;
 590
 591         return rb_left_deepest_node(root->rb_node);
 592 }
 593 EXPORT_SYMBOL(rb_first_postorder);
 594
 595 void rb_link_node_rcu(struct rb_node *node, struct rb_node *parent,
 596                                     struct rb_node **rb_link)
 597 {
 598         node->__rb_parent_color = (unsigned long)parent;
 599         node->rb_left = node->rb_right = NULL;
 600
 601         rcu_assign_pointer(*rb_link, node);
 602 }
 603 EXPORT_SYMBOL(rb_link_node_rcu);