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