tools/lib/rbtree.c

   1 // SPDX-License-Identifier: GPL-2.0-or-later
   2 /*
   3   Red Black Trees
   4   (C) 1999  Andrea Arcangeli <andrea@suse.de>
   5   (C) 2002  David Woodhouse <dwmw2@infradead.org>
   6   (C) 2012  Michel Lespinasse <walken@google.com>
   7
   8
   9   linux/lib/rbtree.c
  10 */
  11
  12 #include <linux/rbtree_augmented.h>
  13 #include <linux/export.h>
  14
  15 /*
  16  * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
  17  *
  18  *  1) A node is either red or black
  19  *  2) The root is black
  20  *  3) All leaves (NULL) are black
  21  *  4) Both children of every red node are black
  22  *  5) Every simple path from root to leaves contains the same number
  23  *     of black nodes.
  24  *
  25  *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
  26  *  consecutive red nodes in a path and every red node is therefore followed by
  27  *  a black. So if B is the number of black nodes on every simple path (as per
  28  *  5), then the longest possible path due to 4 is 2B.
  29  *
  30  *  We shall indicate color with case, where black nodes are uppercase and red
  31  *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
  32  *  parentheses and have some accompanying text comment.
  33  */
  34
  35 /*
  36  * Notes on lockless lookups:
  37  *
  38  * All stores to the tree structure (rb_left and rb_right) must be done using
  39  * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
  40  * tree structure as seen in program order.
  41  *
  42  * These two requirements will allow lockless iteration of the tree -- not
  43  * correct iteration mind you, tree rotations are not atomic so a lookup might
  44  * miss entire subtrees.
  45  *
  46  * But they do guarantee that any such traversal will only see valid elements
  47  * and that it will indeed complete -- does not get stuck in a loop.
  48  *
  49  * It also guarantees that if the lookup returns an element it is the 'correct'
  50  * one. But not returning an element does _NOT_ mean it's not present.
  51  *
  52  * NOTE:
  53  *
  54  * Stores to __rb_parent_color are not important for simple lookups so those
  55  * are left undone as of now. Nor did I check for loops involving parent
  56  * pointers.
  57  */
  58
  59 static inline void rb_set_black(struct rb_node *rb)
  60 {
  61         rb->__rb_parent_color |= RB_BLACK;
  62 }
  63
  64 static inline struct rb_node *rb_red_parent(struct rb_node *red)
  65 {
  66         return (struct rb_node *)red->__rb_parent_color;
  67 }
  68
  69 /*
  70  * Helper function for rotations:
  71  * - old's parent and color get assigned to new
  72  * - old gets assigned new as a parent and 'color' as a color.
  73  */
  74 static inline void
  75 __rb_rotate_set_parents(struct rb_node *old, struct rb_node *new,
  76                         struct rb_root *root, int color)
  77 {
  78         struct rb_node *parent = rb_parent(old);
  79         new->__rb_parent_color = old->__rb_parent_color;
  80         rb_set_parent_color(old, new, color);
  81         __rb_change_child(old, new, parent, root);
  82 }
  83
  84 static __always_inline void
  85 __rb_insert(struct rb_node *node, struct rb_root *root,
  86             bool newleft, struct rb_node **leftmost,
  87             void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
  88 {
  89         struct rb_node *parent = rb_red_parent(node), *gparent, *tmp;
  90
  91         if (newleft)
  92                 *leftmost = node;
  93
  94         while (true) {
  95                 /*
  96                  * Loop invariant: node is red.
  97                  */
  98                 if (unlikely(!parent)) {
  99                         /*
 100                          * The inserted node is root. Either this is the
 101                          * first node, or we recursed at Case 1 below and
 102                          * are no longer violating 4).
 103                          */
 104                         rb_set_parent_color(node, NULL, RB_BLACK);
 105                         break;
 106                 }
 107
 108                 /*
 109                  * If there is a black parent, we are done.
 110                  * Otherwise, take some corrective action as,
 111                  * per 4), we don't want a red root or two
 112                  * consecutive red nodes.
 113                  */
 114                 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 - node's uncle is red (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 - node's uncle is black and node is
 147                                  * the parent's right child (left rotate at parent).
 148                                  *
 149                                  *      G             G
 150                                  *     / \           / \
 151                                  *    p   U  -->    n   U
 152                                  *     \           /
 153                                  *      n         p
 154                                  *
 155                                  * This still leaves us in violation of 4), the
 156                                  * continuation into Case 3 will fix that.
 157                                  */
 158                                 tmp = node->rb_left;
 159                                 WRITE_ONCE(parent->rb_right, tmp);
 160                                 WRITE_ONCE(node->rb_left, parent);
 161                                 if (tmp)
 162                                         rb_set_parent_color(tmp, parent,
 163                                                             RB_BLACK);
 164                                 rb_set_parent_color(parent, node, RB_RED);
 165                                 augment_rotate(parent, node);
 166                                 parent = node;
 167                                 tmp = node->rb_right;
 168                         }
 169
 170                         /*
 171                          * Case 3 - node's uncle is black and node is
 172                          * the parent's left child (right rotate at gparent).
 173                          *
 174                          *        G           P
 175                          *       / \         / \
 176                          *      p   U  -->  n   g
 177                          *     /                 \
 178                          *    n                   U
 179                          */
 180                         WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */
 181                         WRITE_ONCE(parent->rb_right, gparent);
 182                         if (tmp)
 183                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 184                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 185                         augment_rotate(gparent, parent);
 186                         break;
 187                 } else {
 188                         tmp = gparent->rb_left;
 189                         if (tmp && rb_is_red(tmp)) {
 190                                 /* Case 1 - color flips */
 191                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 192                                 rb_set_parent_color(parent, gparent, RB_BLACK);
 193                                 node = gparent;
 194                                 parent = rb_parent(node);
 195                                 rb_set_parent_color(node, parent, RB_RED);
 196                                 continue;
 197                         }
 198
 199                         tmp = parent->rb_left;
 200                         if (node == tmp) {
 201                                 /* Case 2 - right rotate at parent */
 202                                 tmp = node->rb_right;
 203                                 WRITE_ONCE(parent->rb_left, tmp);
 204                                 WRITE_ONCE(node->rb_right, parent);
 205                                 if (tmp)
 206                                         rb_set_parent_color(tmp, parent,
 207                                                             RB_BLACK);
 208                                 rb_set_parent_color(parent, node, RB_RED);
 209                                 augment_rotate(parent, node);
 210                                 parent = node;
 211                                 tmp = node->rb_left;
 212                         }
 213
 214                         /* Case 3 - left rotate at gparent */
 215                         WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */
 216                         WRITE_ONCE(parent->rb_left, gparent);
 217                         if (tmp)
 218                                 rb_set_parent_color(tmp, gparent, RB_BLACK);
 219                         __rb_rotate_set_parents(gparent, parent, root, RB_RED);
 220                         augment_rotate(gparent, parent);
 221                         break;
 222                 }
 223         }
 224 }
 225
 226 /*
 227  * Inline version for rb_erase() use - we want to be able to inline
 228  * and eliminate the dummy_rotate callback there
 229  */
 230 static __always_inline void
 231 ____rb_erase_color(struct rb_node *parent, struct rb_root *root,
 232         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 233 {
 234         struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
 235
 236         while (true) {
 237                 /*
 238                  * Loop invariants:
 239                  * - node is black (or NULL on first iteration)
 240                  * - node is not the root (parent is not NULL)
 241                  * - All leaf paths going through parent and node have a
 242                  *   black node count that is 1 lower than other leaf paths.
 243                  */
 244                 sibling = parent->rb_right;
 245                 if (node != sibling) {  /* node == parent->rb_left */
 246                         if (rb_is_red(sibling)) {
 247                                 /*
 248                                  * Case 1 - left rotate at parent
 249                                  *
 250                                  *     P               S
 251                                  *    / \             / \
 252                                  *   N   s    -->    p   Sr
 253                                  *      / \         / \
 254                                  *     Sl  Sr      N   Sl
 255                                  */
 256                                 tmp1 = sibling->rb_left;
 257                                 WRITE_ONCE(parent->rb_right, tmp1);
 258                                 WRITE_ONCE(sibling->rb_left, parent);
 259                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 260                                 __rb_rotate_set_parents(parent, sibling, root,
 261                                                         RB_RED);
 262                                 augment_rotate(parent, sibling);
 263                                 sibling = tmp1;
 264                         }
 265                         tmp1 = sibling->rb_right;
 266                         if (!tmp1 || rb_is_black(tmp1)) {
 267                                 tmp2 = sibling->rb_left;
 268                                 if (!tmp2 || rb_is_black(tmp2)) {
 269                                         /*
 270                                          * Case 2 - sibling color flip
 271                                          * (p could be either color here)
 272                                          *
 273                                          *    (p)           (p)
 274                                          *    / \           / \
 275                                          *   N   S    -->  N   s
 276                                          *      / \           / \
 277                                          *     Sl  Sr        Sl  Sr
 278                                          *
 279                                          * This leaves us violating 5) which
 280                                          * can be fixed by flipping p to black
 281                                          * if it was red, or by recursing at p.
 282                                          * p is red when coming from Case 1.
 283                                          */
 284                                         rb_set_parent_color(sibling, parent,
 285                                                             RB_RED);
 286                                         if (rb_is_red(parent))
 287                                                 rb_set_black(parent);
 288                                         else {
 289                                                 node = parent;
 290                                                 parent = rb_parent(node);
 291                                                 if (parent)
 292                                                         continue;
 293                                         }
 294                                         break;
 295                                 }
 296                                 /*
 297                                  * Case 3 - right rotate at sibling
 298                                  * (p could be either color here)
 299                                  *
 300                                  *   (p)           (p)
 301                                  *   / \           / \
 302                                  *  N   S    -->  N   sl
 303                                  *     / \             \
 304                                  *    sl  Sr            S
 305                                  *                       \
 306                                  *                        Sr
 307                                  *
 308                                  * Note: p might be red, and then both
 309                                  * p and sl are red after rotation(which
 310                                  * breaks property 4). This is fixed in
 311                                  * Case 4 (in __rb_rotate_set_parents()
 312                                  *         which set sl the color of p
 313                                  *         and set p RB_BLACK)
 314                                  *
 315                                  *   (p)            (sl)
 316                                  *   / \            /  \
 317                                  *  N   sl   -->   P    S
 318                                  *       \        /      \
 319                                  *        S      N        Sr
 320                                  *         \
 321                                  *          Sr
 322                                  */
 323                                 tmp1 = tmp2->rb_right;
 324                                 WRITE_ONCE(sibling->rb_left, tmp1);
 325                                 WRITE_ONCE(tmp2->rb_right, sibling);
 326                                 WRITE_ONCE(parent->rb_right, tmp2);
 327                                 if (tmp1)
 328                                         rb_set_parent_color(tmp1, sibling,
 329                                                             RB_BLACK);
 330                                 augment_rotate(sibling, tmp2);
 331                                 tmp1 = sibling;
 332                                 sibling = tmp2;
 333                         }
 334                         /*
 335                          * Case 4 - left rotate at parent + color flips
 336                          * (p and sl could be either color here.
 337                          *  After rotation, p becomes black, s acquires
 338                          *  p's color, and sl keeps its color)
 339                          *
 340                          *      (p)             (s)
 341                          *      / \             / \
 342                          *     N   S     -->   P   Sr
 343                          *        / \         / \
 344                          *      (sl) sr      N  (sl)
 345                          */
 346                         tmp2 = sibling->rb_left;
 347                         WRITE_ONCE(parent->rb_right, tmp2);
 348                         WRITE_ONCE(sibling->rb_left, parent);
 349                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 350                         if (tmp2)
 351                                 rb_set_parent(tmp2, parent);
 352                         __rb_rotate_set_parents(parent, sibling, root,
 353                                                 RB_BLACK);
 354                         augment_rotate(parent, sibling);
 355                         break;
 356                 } else {
 357                         sibling = parent->rb_left;
 358                         if (rb_is_red(sibling)) {
 359                                 /* Case 1 - right rotate at parent */
 360                                 tmp1 = sibling->rb_right;
 361                                 WRITE_ONCE(parent->rb_left, tmp1);
 362                                 WRITE_ONCE(sibling->rb_right, parent);
 363                                 rb_set_parent_color(tmp1, parent, RB_BLACK);
 364                                 __rb_rotate_set_parents(parent, sibling, root,
 365                                                         RB_RED);
 366                                 augment_rotate(parent, sibling);
 367                                 sibling = tmp1;
 368                         }
 369                         tmp1 = sibling->rb_left;
 370                         if (!tmp1 || rb_is_black(tmp1)) {
 371                                 tmp2 = sibling->rb_right;
 372                                 if (!tmp2 || rb_is_black(tmp2)) {
 373                                         /* Case 2 - sibling color flip */
 374                                         rb_set_parent_color(sibling, parent,
 375                                                             RB_RED);
 376                                         if (rb_is_red(parent))
 377                                                 rb_set_black(parent);
 378                                         else {
 379                                                 node = parent;
 380                                                 parent = rb_parent(node);
 381                                                 if (parent)
 382                                                         continue;
 383                                         }
 384                                         break;
 385                                 }
 386                                 /* Case 3 - left rotate at sibling */
 387                                 tmp1 = tmp2->rb_left;
 388                                 WRITE_ONCE(sibling->rb_right, tmp1);
 389                                 WRITE_ONCE(tmp2->rb_left, sibling);
 390                                 WRITE_ONCE(parent->rb_left, tmp2);
 391                                 if (tmp1)
 392                                         rb_set_parent_color(tmp1, sibling,
 393                                                             RB_BLACK);
 394                                 augment_rotate(sibling, tmp2);
 395                                 tmp1 = sibling;
 396                                 sibling = tmp2;
 397                         }
 398                         /* Case 4 - right rotate at parent + color flips */
 399                         tmp2 = sibling->rb_right;
 400                         WRITE_ONCE(parent->rb_left, tmp2);
 401                         WRITE_ONCE(sibling->rb_right, parent);
 402                         rb_set_parent_color(tmp1, sibling, RB_BLACK);
 403                         if (tmp2)
 404                                 rb_set_parent(tmp2, parent);
 405                         __rb_rotate_set_parents(parent, sibling, root,
 406                                                 RB_BLACK);
 407                         augment_rotate(parent, sibling);
 408                         break;
 409                 }
 410         }
 411 }
 412
 413 /* Non-inline version for rb_erase_augmented() use */
 414 void __rb_erase_color(struct rb_node *parent, struct rb_root *root,
 415         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 416 {
 417         ____rb_erase_color(parent, root, augment_rotate);
 418 }
 419
 420 /*
 421  * Non-augmented rbtree manipulation functions.
 422  *
 423  * We use dummy augmented callbacks here, and have the compiler optimize them
 424  * out of the rb_insert_color() and rb_erase() function definitions.
 425  */
 426
 427 static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
 428 static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
 429 static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
 430
 431 static const struct rb_augment_callbacks dummy_callbacks = {
 432         .propagate = dummy_propagate,
 433         .copy = dummy_copy,
 434         .rotate = dummy_rotate
 435 };
 436
 437 void rb_insert_color(struct rb_node *node, struct rb_root *root)
 438 {
 439         __rb_insert(node, root, false, NULL, dummy_rotate);
 440 }
 441
 442 void rb_erase(struct rb_node *node, struct rb_root *root)
 443 {
 444         struct rb_node *rebalance;
 445         rebalance = __rb_erase_augmented(node, root,
 446                                          NULL, &dummy_callbacks);
 447         if (rebalance)
 448                 ____rb_erase_color(rebalance, root, dummy_rotate);
 449 }
 450
 451 void rb_insert_color_cached(struct rb_node *node,
 452                             struct rb_root_cached *root, bool leftmost)
 453 {
 454         __rb_insert(node, &root->rb_root, leftmost,
 455                     &root->rb_leftmost, dummy_rotate);
 456 }
 457
 458 void rb_erase_cached(struct rb_node *node, struct rb_root_cached *root)
 459 {
 460         struct rb_node *rebalance;
 461         rebalance = __rb_erase_augmented(node, &root->rb_root,
 462                                          &root->rb_leftmost, &dummy_callbacks);
 463         if (rebalance)
 464                 ____rb_erase_color(rebalance, &root->rb_root, dummy_rotate);
 465 }
 466
 467 /*
 468  * Augmented rbtree manipulation functions.
 469  *
 470  * This instantiates the same __always_inline functions as in the non-augmented
 471  * case, but this time with user-defined callbacks.
 472  */
 473
 474 void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
 475                            bool newleft, struct rb_node **leftmost,
 476         void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 477 {
 478         __rb_insert(node, root, newleft, leftmost, augment_rotate);
 479 }
 480
 481 /*
 482  * This function returns the first node (in sort order) of the tree.
 483  */
 484 struct rb_node *rb_first(const struct rb_root *root)
 485 {
 486         struct rb_node  *n;
 487
 488         n = root->rb_node;
 489         if (!n)
 490                 return NULL;
 491         while (n->rb_left)
 492                 n = n->rb_left;
 493         return n;
 494 }
 495
 496 struct rb_node *rb_last(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_right)
 504                 n = n->rb_right;
 505         return n;
 506 }
 507
 508 struct rb_node *rb_next(const struct rb_node *node)
 509 {
 510         struct rb_node *parent;
 511
 512         if (RB_EMPTY_NODE(node))
 513                 return NULL;
 514
 515         /*
 516          * If we have a right-hand child, go down and then left as far
 517          * as we can.
 518          */
 519         if (node->rb_right) {
 520                 node = node->rb_right;
 521                 while (node->rb_left)
 522                         node=node->rb_left;
 523                 return (struct rb_node *)node;
 524         }
 525
 526         /*
 527          * No right-hand children. Everything down and left is smaller than us,
 528          * so any 'next' node must be in the general direction of our parent.
 529          * Go up the tree; any time the ancestor is a right-hand child of its
 530          * parent, keep going up. First time it's a left-hand child of its
 531          * parent, said parent is our 'next' node.
 532          */
 533         while ((parent = rb_parent(node)) && node == parent->rb_right)
 534                 node = parent;
 535
 536         return parent;
 537 }
 538
 539 struct rb_node *rb_prev(const struct rb_node *node)
 540 {
 541         struct rb_node *parent;
 542
 543         if (RB_EMPTY_NODE(node))
 544                 return NULL;
 545
 546         /*
 547          * If we have a left-hand child, go down and then right as far
 548          * as we can.
 549          */
 550         if (node->rb_left) {
 551                 node = node->rb_left;
 552                 while (node->rb_right)
 553                         node=node->rb_right;
 554                 return (struct rb_node *)node;
 555         }
 556
 557         /*
 558          * No left-hand children. Go up till we find an ancestor which
 559          * is a right-hand child of its parent.
 560          */
 561         while ((parent = rb_parent(node)) && node == parent->rb_left)
 562                 node = parent;
 563
 564         return parent;
 565 }
 566
 567 void rb_replace_node(struct rb_node *victim, struct rb_node *new,
 568                      struct rb_root *root)
 569 {
 570         struct rb_node *parent = rb_parent(victim);
 571
 572         /* Copy the pointers/colour from the victim to the replacement */
 573         *new = *victim;
 574
 575         /* Set the surrounding nodes to point to the replacement */
 576         if (victim->rb_left)
 577                 rb_set_parent(victim->rb_left, new);
 578         if (victim->rb_right)
 579                 rb_set_parent(victim->rb_right, new);
 580         __rb_change_child(victim, new, parent, root);
 581 }
 582
 583 void rb_replace_node_cached(struct rb_node *victim, struct rb_node *new,
 584                             struct rb_root_cached *root)
 585 {
 586         rb_replace_node(victim, new, &root->rb_root);
 587
 588         if (root->rb_leftmost == victim)
 589                 root->rb_leftmost = new;
 590 }
 591
 592 static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
 593 {
 594         for (;;) {
 595                 if (node->rb_left)
 596                         node = node->rb_left;
 597                 else if (node->rb_right)
 598                         node = node->rb_right;
 599                 else
 600                         return (struct rb_node *)node;
 601         }
 602 }
 603
 604 struct rb_node *rb_next_postorder(const struct rb_node *node)
 605 {
 606         const struct rb_node *parent;
 607         if (!node)
 608                 return NULL;
 609         parent = rb_parent(node);
 610
 611         /* If we're sitting on node, we've already seen our children */
 612         if (parent && node == parent->rb_left && parent->rb_right) {
 613                 /* If we are the parent's left node, go to the parent's right
 614                  * node then all the way down to the left */
 615                 return rb_left_deepest_node(parent->rb_right);
 616         } else
 617                 /* Otherwise we are the parent's right node, and the parent
 618                  * should be next */
 619                 return (struct rb_node *)parent;
 620 }
 621
 622 struct rb_node *rb_first_postorder(const struct rb_root *root)
 623 {
 624         if (!root->rb_node)
 625                 return NULL;
 626
 627         return rb_left_deepest_node(root->rb_node);
 628 }