tools/lib/rbtree.c

   1 /*
   2   Red Black Trees
   3   (C) 1999  Andrea Arcangeli <[email protected]>
   4   (C) 2002  David Woodhouse <[email protected]>
   5   (C) 2012  Michel Lespinasse <[email protected]>
   6
   7   This program is free software; you can redistribute it and/or modify
   8   it under the terms of the GNU General Public License as published by
   9   the Free Software Foundation; either version 2 of the License, or
  10   (at your option) any later version.
  11
  12   This program is distributed in the hope that it will be useful,
  13   but WITHOUT ANY WARRANTY; without even the implied warranty of
  14   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15   GNU General Public License for more details.
  16
  17   You should have received a copy of the GNU General Public License
  18   along with this program; if not, write to the Free Software
  19   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  20
  21   linux/lib/rbtree.c
  22 */
  23
  24 #include <linux/rbtree_augmented.h>
  25 #include <linux/export.h>
  26
  27 /*
  28  * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
  29  *
  30  *  1) A node is either red or black
  31  *  2) The root is black
  32  *  3) All leaves (NULL) are black
  33  *  4) Both children of every red node are black
  34  *  5) Every simple path from root to leaves contains the same number
  35  *     of black nodes.
  36  *
  37  *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
  38  *  consecutive red nodes in a path and every red node is therefore followed by
  39  *  a black. So if B is the number of black nodes on every simple path (as per
  40  *  5), then the longest possible path due to 4 is 2B.
  41  *
  42  *  We shall indicate color with case, where black nodes are uppercase and red
  43  *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
  44  *  parentheses and have some accompanying text comment.
  45  */
  46
  47 /*
  48  * Notes on lockless lookups:
  49  *
  50  * All stores to the tree structure (rb_left and rb_right) must be done using
  51  * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
  52  * tree structure as seen in program order.
  53  *
  54  * These two requirements will allow lockless iteration of the tree -- not
  55  * correct iteration mind you, tree rotations are not atomic so a lookup might
  56  * miss entire subtrees.
  57  *
  58  * But they do guarantee that any such traversal will only see valid elements
  59  * and that it will indeed complete -- does not get stuck in a loop.
  60  *
  61  * It also guarantees that if the lookup returns an element it is the 'correct'
  62  * one. But not returning an element does _NOT_ mean it's not present.
  63  *
  64  * NOTE:
  65  *
  66  * Stores to __rb_parent_color are not important for simple lookups so those
  67  * are left undone as of now. Nor did I check for loops involving parent
  68  * pointers.
  69  */
  70
  71 static inline void rb_set_black(struct rb_node *rb)
  72 {
  73         rb->__rb_parent_color |= RB_BLACK;
  74 }
  75
  76 static inline struct rb_node *rb_red_parent(struct rb_node *red)
  77 {
  78         return (struct rb_node *)red->__rb_parent_color;
  79 }
  80
  81 /*
  82  * Helper function for rotations:
  83  * - old's parent and color get assigned to new
  84  * - old gets assigned new as a parent and 'color' as a color.
  85  */
  86 static inline void
  87 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
  88                         struct rb_root *root, int color)
  89 {
  90         struct rb_node *parent = rb_parent(old);
  91         new->__rb_parent_color = old->__rb_parent_color;
  92         rb_set_parent_color(old, new, color);
  93         __rb_change_child(old, new, parent, root);
  94 }
  95
  96 static __always_inline void
  97 __rb_insert(struct rb_node *node, struct rb_root *root,
  98             bool newleft, struct rb_node **leftmost,
  99             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 100 {
 101         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
 102
 103         if (newleft)
 104                 *leftmost = node;
 105
 106         while (true) {
 107                 /*
 108                  * Loop invariant: node is red.
 109                  */
 110                 if (unlikely(!parent)) {
 111                         /*
 112                          * The inserted node is root. Either this is the
 113                          * first node, or we recursed at Case 1 below and
 114                          * are no longer violating 4).
 115                          */
 116                         rb_set_parent_color(node, NULL, RB_BLACK);
 117                         break;
 118                 }
 119
 120                 /*
 121                  * If there is a black parent, we are done.
 122                  * Otherwise, take some corrective action as,
 123                  * per 4), we don't want a red root or two
 124                  * consecutive red nodes.
 125                  */
 126                 if(rb_is_black(parent))
 127                         break;
 128
 129                 gparent = rb_red_parent(parent);
 130
 131                 tmp = gparent->rb_right;
 132                 if (parent != tmp) {    /* parent == gparent->rb_left */
 133                         if (tmp && rb_is_red(tmp)) {
 134                                 /*
 135                                  * Case 1 - node's uncle is red (color flips).
 136                                  *
 137                                  *       G            g
 138                                  *      / \          / \
 139                                  *     p   u  -->   P   U
 140                                  *    /            /
 141                                  *   n            n
 142                                  *
 143                                  * However, since g's parent might be red, and
 144                                  * 4) does not allow this, we need to recurse
 145                                  * at g.
 146                                  */
 147                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 148                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 149                                 node = gparent;
 150                                 parent = rb_parent(node);
 151                                 rb_set_parent_color(node, parent, RB_RED);
 152                                 continue;
 153                         }
 154
 155                         tmp = parent->rb_right;
 156                         if (node == tmp) {
 157                                 /*
 158                                  * Case 2 - node's uncle is black and node is
 159                                  * the parent's right child (left rotate at parent).
 160                                  *
 161                                  *      G             G
 162                                  *     / \           / \
 163                                  *    p   U  -->    n   U
 164                                  *     \           /
 165                                  *      n         p
 166                                  *
 167                                  * This still leaves us in violation of 4), the
 168                                  * continuation into Case 3 will fix that.
 169                                  */
 170                                 tmp = node->rb_left;
 171                                 WRITE_ONCE(parent->rb_right, tmp);
 172                                 WRITE_ONCE(node->rb_left, parent);
 173                                 if (tmp)
 174                                         rb_set_parent_color(tmp, parent,
 175                                                             RB_BLACK);
 176                                 rb_set_parent_color(parent, node, RB_RED);
 177                                 augment_rotate(parent, node);
 178                                 parent = node;
 179                                 tmp = node->rb_right;
 180                         }
 181
 182                         /*
 183                          * Case 3 - node's uncle is black and node is
 184                          * the parent's left child (right rotate at gparent).
 185                          *
 186                          *        G           P
 187                          *       / \         / \
 188                          *      p   U  -->  n   g
 189                          *     /                 \
 190                          *    n                   U
 191                          */
 192                         WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
 193                         WRITE_ONCE(parent->rb_right, gparent);
 194                         if (tmp)
 195                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 196                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 197                         augment_rotate(gparent, parent);
 198                         break;
 199                 } else {
 200                         tmp = gparent->rb_left;
 201                         if (tmp && rb_is_red(tmp)) {
 202                                 /* Case 1 - color flips */
 203                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 204                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 205                                 node = gparent;
 206                                 parent = rb_parent(node);
 207                                 rb_set_parent_color(node, parent, RB_RED);
 208                                 continue;
 209                         }
 210
 211                         tmp = parent->rb_left;
 212                         if (node == tmp) {
 213                                 /* Case 2 - right rotate at parent */
 214                                 tmp = node->rb_right;
 215                                 WRITE_ONCE(parent->rb_left, tmp);
 216                                 WRITE_ONCE(node->rb_right, parent);
 217                                 if (tmp)
 218                                         rb_set_parent_color(tmp, parent,
 219                                                             RB_BLACK);
 220                                 rb_set_parent_color(parent, node, RB_RED);
 221                                 augment_rotate(parent, node);
 222                                 parent = node;
 223                                 tmp = node->rb_left;
 224                         }
 225
 226                         /* Case 3 - left rotate at gparent */
 227                         WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
 228                         WRITE_ONCE(parent->rb_left, gparent);
 229                         if (tmp)
 230                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 231                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 232                         augment_rotate(gparent, parent);
 233                         break;
 234                 }
 235         }
 236 }
 237
 238 /*
 239  * Inline version for rb_erase() use - we want to be able to inline
 240  * and eliminate the dummy_rotate callback there
 241  */
 242 static __always_inline void
 243 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
 244         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 245 {
 246         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
 247
 248         while (true) {
 249                 /*
 250                  * Loop invariants:
 251                  * - node is black (or NULL on first iteration)
 252                  * - node is not the root (parent is not NULL)
 253                  * - All leaf paths going through parent and node have a
 254                  *   black node count that is 1 lower than other leaf paths.
 255                  */
 256                 sibling = parent->rb_right;
 257                 if (node != sibling) {  /* node == parent->rb_left */
 258                         if (rb_is_red(sibling)) {
 259                                 /*
 260                                  * Case 1 - left rotate at parent
 261                                  *
 262                                  *     P               S
 263                                  *    / \             / \
 264                                  *   N   s    -->    p   Sr
 265                                  *      / \         / \
 266                                  *     Sl  Sr      N   Sl
 267                                  */
 268                                 tmp1 = sibling->rb_left;
 269                                 WRITE_ONCE(parent->rb_right, tmp1);
 270                                 WRITE_ONCE(sibling->rb_left, parent);
 271                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 272                                 __rb_rotate_set_parents(parent, sibling, root,
 273                                                         RB_RED);
 274                                 augment_rotate(parent, sibling);
 275                                 sibling = tmp1;
 276                         }
 277                         tmp1 = sibling->rb_right;
 278                         if (!tmp1 || rb_is_black(tmp1)) {
 279                                 tmp2 = sibling->rb_left;
 280                                 if (!tmp2 || rb_is_black(tmp2)) {
 281                                         /*
 282                                          * Case 2 - sibling color flip
 283                                          * (p could be either color here)
 284                                          *
 285                                          *    (p)           (p)
 286                                          *    / \           / \
 287                                          *   N   S    -->  N   s
 288                                          *      / \           / \
 289                                          *     Sl  Sr        Sl  Sr
 290                                          *
 291                                          * This leaves us violating 5) which
 292                                          * can be fixed by flipping p to black
 293                                          * if it was red, or by recursing at p.
 294                                          * p is red when coming from Case 1.
 295                                          */
 296                                         rb_set_parent_color(sibling, parent,
 297                                                             RB_RED);
 298                                         if (rb_is_red(parent))
 299                                                 rb_set_black(parent);
 300                                         else {
 301                                                 node = parent;
 302                                                 parent = rb_parent(node);
 303                                                 if (parent)
 304                                                         continue;
 305                                         }
 306                                         break;
 307                                 }
 308                                 /*
 309                                  * Case 3 - right rotate at sibling
 310                                  * (p could be either color here)
 311                                  *
 312                                  *   (p)           (p)
 313                                  *   / \           / \
 314                                  *  N   S    -->  N   sl
 315                                  *     / \             \
 316                                  *    sl  Sr            S
 317                                  *                       \
 318                                  *                        Sr
 319                                  *
 320                                  * Note: p might be red, and then both
 321                                  * p and sl are red after rotation(which
 322                                  * breaks property 4). This is fixed in
 323                                  * Case 4 (in __rb_rotate_set_parents()
 324                                  *         which set sl the color of p
 325                                  *         and set p RB_BLACK)
 326                                  *
 327                                  *   (p)            (sl)
 328                                  *   / \            /  \
 329                                  *  N   sl   -->   P    S
 330                                  *       \        /      \
 331                                  *        S      N        Sr
 332                                  *         \
 333                                  *          Sr
 334                                  */
 335                                 tmp1 = tmp2->rb_right;
 336                                 WRITE_ONCE(sibling->rb_left, tmp1);
 337                                 WRITE_ONCE(tmp2->rb_right, sibling);
 338                                 WRITE_ONCE(parent->rb_right, tmp2);
 339                                 if (tmp1)
 340                                         rb_set_parent_color(tmp1, sibling,
 341                                                             RB_BLACK);
 342                                 augment_rotate(sibling, tmp2);
 343                                 tmp1 = sibling;
 344                                 sibling = tmp2;
 345                         }
 346                         /*
 347                          * Case 4 - left rotate at parent + color flips
 348                          * (p and sl could be either color here.
 349                          *  After rotation, p becomes black, s acquires
 350                          *  p's color, and sl keeps its color)
 351                          *
 352                          *      (p)             (s)
 353                          *      / \             / \
 354                          *     N   S     -->   P   Sr
 355                          *        / \         / \
 356                          *      (sl) sr      N  (sl)
 357                          */
 358                         tmp2 = sibling->rb_left;
 359                         WRITE_ONCE(parent->rb_right, tmp2);
 360                         WRITE_ONCE(sibling->rb_left, parent);
 361                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 362                         if (tmp2)
 363                                 rb_set_parent(tmp2, parent);
 364                         __rb_rotate_set_parents(parent, sibling, root,
 365                                                 RB_BLACK);
 366                         augment_rotate(parent, sibling);
 367                         break;
 368                 } else {
 369                         sibling = parent->rb_left;
 370                         if (rb_is_red(sibling)) {
 371                                 /* Case 1 - right rotate at parent */
 372                                 tmp1 = sibling->rb_right;
 373                                 WRITE_ONCE(parent->rb_left, tmp1);
 374                                 WRITE_ONCE(sibling->rb_right, parent);
 375                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 376                                 __rb_rotate_set_parents(parent, sibling, root,
 377                                                         RB_RED);
 378                                 augment_rotate(parent, sibling);
 379                                 sibling = tmp1;
 380                         }
 381                         tmp1 = sibling->rb_left;
 382                         if (!tmp1 || rb_is_black(tmp1)) {
 383                                 tmp2 = sibling->rb_right;
 384                                 if (!tmp2 || rb_is_black(tmp2)) {
 385                                         /* Case 2 - sibling color flip */
 386                                         rb_set_parent_color(sibling, parent,
 387                                                             RB_RED);
 388                                         if (rb_is_red(parent))
 389                                                 rb_set_black(parent);
 390                                         else {
 391                                                 node = parent;
 392                                                 parent = rb_parent(node);
 393                                                 if (parent)
 394                                                         continue;
 395                                         }
 396                                         break;
 397                                 }
 398                                 /* Case 3 - left rotate at sibling */
 399                                 tmp1 = tmp2->rb_left;
 400                                 WRITE_ONCE(sibling->rb_right, tmp1);
 401                                 WRITE_ONCE(tmp2->rb_left, sibling);
 402                                 WRITE_ONCE(parent->rb_left, tmp2);
 403                                 if (tmp1)
 404                                         rb_set_parent_color(tmp1, sibling,
 405                                                             RB_BLACK);
 406                                 augment_rotate(sibling, tmp2);
 407                                 tmp1 = sibling;
 408                                 sibling = tmp2;
 409                         }
 410                         /* Case 4 - right rotate at parent + color flips */
 411                         tmp2 = sibling->rb_right;
 412                         WRITE_ONCE(parent->rb_left, tmp2);
 413                         WRITE_ONCE(sibling->rb_right, parent);
 414                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 415                         if (tmp2)
 416                                 rb_set_parent(tmp2, parent);
 417                         __rb_rotate_set_parents(parent, sibling, root,
 418                                                 RB_BLACK);
 419                         augment_rotate(parent, sibling);
 420                         break;
 421                 }
 422         }
 423 }
 424
 425 /* Non-inline version for rb_erase_augmented() use */
 426 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
 427         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 428 {
 429         ____rb_erase_color(parent, root, augment_rotate);
 430 }
 431
 432 /*
 433  * Non-augmented rbtree manipulation functions.
 434  *
 435  * We use dummy augmented callbacks here, and have the compiler optimize them
 436  * out of the rb_insert_color() and rb_erase() function definitions.
 437  */
 438
 439 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
 440 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
 441 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
 442
 443 static const struct rb_augment_callbacks dummy_callbacks = {
 444         .propagate = dummy_propagate,
 445         .copy = dummy_copy,
 446         .rotate = dummy_rotate
 447 };
 448
 449 void rb_insert_color(struct rb_node *node, struct rb_root *root)
 450 {
 451         __rb_insert(node, root, false, NULL, dummy_rotate);
 452 }
 453
 454 void rb_erase(struct rb_node *node, struct rb_root *root)
 455 {
 456         struct rb_node *rebalance;
 457         rebalance = __rb_erase_augmented(node, root,
 458                                          NULL, &dummy_callbacks);
 459         if (rebalance)
 460                 ____rb_erase_color(rebalance, root, dummy_rotate);
 461 }
 462
 463 void rb_insert_color_cached(struct rb_node *node,
 464                             struct rb_root_cached *root, bool leftmost)
 465 {
 466         __rb_insert(node, &root->rb_root, leftmost,
 467                     &root->rb_leftmost, dummy_rotate);
 468 }
 469
 470 void rb_erase_cached(struct rb_node *node, struct rb_root_cached *root)
 471 {
 472         struct rb_node *rebalance;
 473         rebalance = __rb_erase_augmented(node, &root->rb_root,
 474                                          &root->rb_leftmost, &dummy_callbacks);
 475         if (rebalance)
 476                 ____rb_erase_color(rebalance, &root->rb_root, dummy_rotate);
 477 }
 478
 479 /*
 480  * Augmented rbtree manipulation functions.
 481  *
 482  * This instantiates the same __always_inline functions as in the non-augmented
 483  * case, but this time with user-defined callbacks.
 484  */
 485
 486 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
 487                            bool newleft, struct rb_node **leftmost,
 488         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 489 {
 490         __rb_insert(node, root, newleft, leftmost, augment_rotate);
 491 }
 492
 493 /*
 494  * This function returns the first node (in sort order) of the tree.
 495  */
 496 struct rb_node *rb_first(const struct rb_root *root)
 497 {
 498         struct rb_node  *n;
 499
 500         n = root->rb_node;
 501         if (!n)
 502                 return NULL;
 503         while (n->rb_left)
 504                 n = n->rb_left;
 505         return n;
 506 }
 507
 508 struct rb_node *rb_last(const struct rb_root *root)
 509 {
 510         struct rb_node  *n;
 511
 512         n = root->rb_node;
 513         if (!n)
 514                 return NULL;
 515         while (n->rb_right)
 516                 n = n->rb_right;
 517         return n;
 518 }
 519
 520 struct rb_node *rb_next(const struct rb_node *node)
 521 {
 522         struct rb_node *parent;
 523
 524         if (RB_EMPTY_NODE(node))
 525                 return NULL;
 526
 527         /*
 528          * If we have a right-hand child, go down and then left as far
 529          * as we can.
 530          */
 531         if (node->rb_right) {
 532                 node = node->rb_right;
 533                 while (node->rb_left)
 534                         node=node->rb_left;
 535                 return (struct rb_node *)node;
 536         }
 537
 538         /*
 539          * No right-hand children. Everything down and left is smaller than us,
 540          * so any 'next' node must be in the general direction of our parent.
 541          * Go up the tree; any time the ancestor is a right-hand child of its
 542          * parent, keep going up. First time it's a left-hand child of its
 543          * parent, said parent is our 'next' node.
 544          */
 545         while ((parent = rb_parent(node)) && node == parent->rb_right)
 546                 node = parent;
 547
 548         return parent;
 549 }
 550
 551 struct rb_node *rb_prev(const struct rb_node *node)
 552 {
 553         struct rb_node *parent;
 554
 555         if (RB_EMPTY_NODE(node))
 556                 return NULL;
 557
 558         /*
 559          * If we have a left-hand child, go down and then right as far
 560          * as we can.
 561          */
 562         if (node->rb_left) {
 563                 node = node->rb_left;
 564                 while (node->rb_right)
 565                         node=node->rb_right;
 566                 return (struct rb_node *)node;
 567         }
 568
 569         /*
 570          * No left-hand children. Go up till we find an ancestor which
 571          * is a right-hand child of its parent.
 572          */
 573         while ((parent = rb_parent(node)) && node == parent->rb_left)
 574                 node = parent;
 575
 576         return parent;
 577 }
 578
 579 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
 580                      struct rb_root *root)
 581 {
 582         struct rb_node *parent = rb_parent(victim);
 583
 584         /* Copy the pointers/colour from the victim to the replacement */
 585         *new = *victim;
 586
 587         /* Set the surrounding nodes to point to the replacement */
 588         if (victim->rb_left)
 589                 rb_set_parent(victim->rb_left, new);
 590         if (victim->rb_right)
 591                 rb_set_parent(victim->rb_right, new);
 592         __rb_change_child(victim, new, parent, root);
 593 }
 594
 595 void rb_replace_node_cached(struct rb_node *victim, struct rb_node *new,
 596                             struct rb_root_cached *root)
 597 {
 598         rb_replace_node(victim, new, &root->rb_root);
 599
 600         if (root->rb_leftmost == victim)
 601                 root->rb_leftmost = new;
 602 }
 603
 604 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
 605 {
 606         for (;;) {
 607                 if (node->rb_left)
 608                         node = node->rb_left;
 609                 else if (node->rb_right)
 610                         node = node->rb_right;
 611                 else
 612                         return (struct rb_node *)node;
 613         }
 614 }
 615
 616 struct rb_node *rb_next_postorder(const struct rb_node *node)
 617 {
 618         const struct rb_node *parent;
 619         if (!node)
 620                 return NULL;
 621         parent = rb_parent(node);
 622
 623         /* If we're sitting on node, we've already seen our children */
 624         if (parent && node == parent->rb_left && parent->rb_right) {
 625                 /* If we are the parent's left node, go to the parent's right
 626                  * node then all the way down to the left */
 627                 return rb_left_deepest_node(parent->rb_right);
 628         } else
 629                 /* Otherwise we are the parent's right node, and the parent
 630                  * should be next */
 631                 return (struct rb_node *)parent;
 632 }
 633
 634 struct rb_node *rb_first_postorder(const struct rb_root *root)
 635 {
 636         if (!root->rb_node)
 637                 return NULL;
 638
 639         return rb_left_deepest_node(root->rb_node);
 640 }