LXR linux/lib/rbtree.c

   1/*
   2  Red Black Trees
   3  (C) 1999  Andrea Arcangeli <andrea@suse.de>
   4  (C) 2002  David Woodhouse <dwmw2@infradead.org>
   5  (C) 2012  Michel Lespinasse <walken@google.com>
   6
   7  This program is free software; you can redistribute it and/or modify
   8  it under the terms of the GNU General Public License as published by
   9  the Free Software Foundation; either version 2 of the License, or
  10  (at your option) any later version.
  11
  12  This program is distributed in the hope that it will be useful,
  13  but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15  GNU General Public License for more details.
  16
  17  You should have received a copy of the GNU General Public License
  18  along with this program; if not, write to the Free Software
  19  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  20
  21  linux/lib/rbtree.c
  22*/
  23
  24#include <linux/rbtree_augmented.h>
  25#include <linux/export.h>
  26
  27/*
  28 * red-black trees properties:  http://en.wikipedia.org/wiki/Rbtree
  29 *
  30 *  1) A node is either red or black
  31 *  2) The root is black
  32 *  3) All leaves (NULL) are black
  33 *  4) Both children of every red node are black
  34 *  5) Every simple path from root to leaves contains the same number
  35 *     of black nodes.
  36 *
  37 *  4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two
  38 *  consecutive red nodes in a path and every red node is therefore followed by
  39 *  a black. So if B is the number of black nodes on every simple path (as per
  40 *  5), then the longest possible path due to 4 is 2B.
  41 *
  42 *  We shall indicate color with case, where black nodes are uppercase and red
  43 *  nodes will be lowercase. Unknown color nodes shall be drawn as red within
  44 *  parentheses and have some accompanying text comment.
  45 */
  46
  47/*
  48 * Notes on lockless lookups:
  49 *
  50 * All stores to the tree structure (rb_left and rb_right) must be done using
  51 * WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the
  52 * tree structure as seen in program order.
  53 *
  54 * These two requirements will allow lockless iteration of the tree -- not
  55 * correct iteration mind you, tree rotations are not atomic so a lookup might
  56 * miss entire subtrees.
  57 *
  58 * But they do guarantee that any such traversal will only see valid elements
  59 * and that it will indeed complete -- does not get stuck in a loop.
  60 *
  61 * It also guarantees that if the lookup returns an element it is the 'correct'
  62 * one. But not returning an element does _NOT_ mean it's not present.
  63 *
  64 * NOTE:
  65 *
  66 * Stores to __rb_parent_color are not important for simple lookups so those
  67 * are left undone as of now. Nor did I check for loops involving parent
  68 * pointers.
  69 */
  70
  71static inline void rb_set_black(struct rb_node *rb)
  72{
  73        rb->__rb_parent_color |= RB_BLACK;
  74}
  75
  76static 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 */
  86static 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
  96static __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 */
 242static __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 */
 426void __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}
 431EXPORT_SYMBOL(__rb_erase_color);
 432
 433/*
 434 * Non-augmented rbtree manipulation functions.
 435 *
 436 * We use dummy augmented callbacks here, and have the compiler optimize them
 437 * out of the rb_insert_color() and rb_erase() function definitions.
 438 */
 439
 440static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {}
 441static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
 442static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
 443
 444static const struct rb_augment_callbacks dummy_callbacks = {
 445        .propagate = dummy_propagate,
 446        .copy = dummy_copy,
 447        .rotate = dummy_rotate
 448};
 449
 450void rb_insert_color(struct rb_node *node, struct rb_root *root)
 451{
 452        __rb_insert(node, root, false, NULL, dummy_rotate);
 453}
 454EXPORT_SYMBOL(rb_insert_color);
 455
 456void rb_erase(struct rb_node *node, struct rb_root *root)
 457{
 458        struct rb_node *rebalance;
 459        rebalance = __rb_erase_augmented(node, root,
 460                                         NULL, &dummy_callbacks);
 461        if (rebalance)
 462                ____rb_erase_color(rebalance, root, dummy_rotate);
 463}
 464EXPORT_SYMBOL(rb_erase);
 465
 466void rb_insert_color_cached(struct rb_node *node,
 467                            struct rb_root_cached *root, bool leftmost)
 468{
 469        __rb_insert(node, &root->rb_root, leftmost,
 470                    &root->rb_leftmost, dummy_rotate);
 471}
 472EXPORT_SYMBOL(rb_insert_color_cached);
 473
 474void rb_erase_cached(struct rb_node *node, struct rb_root_cached *root)
 475{
 476        struct rb_node *rebalance;
 477        rebalance = __rb_erase_augmented(node, &root->rb_root,
 478                                         &root->rb_leftmost, &dummy_callbacks);
 479        if (rebalance)
 480                ____rb_erase_color(rebalance, &root->rb_root, dummy_rotate);
 481}
 482EXPORT_SYMBOL(rb_erase_cached);
 483
 484/*
 485 * Augmented rbtree manipulation functions.
 486 *
 487 * This instantiates the same __always_inline functions as in the non-augmented
 488 * case, but this time with user-defined callbacks.
 489 */
 490
 491void __rb_insert_augmented(struct rb_node *node, struct rb_root *root,
 492                           bool newleft, struct rb_node **leftmost,
 493        void (*augment_rotate)(struct rb_node *old, struct rb_node *new))
 494{
 495        __rb_insert(node, root, newleft, leftmost, augment_rotate);
 496}
 497EXPORT_SYMBOL(__rb_insert_augmented);
 498
 499/*
 500 * This function returns the first node (in sort order) of the tree.
 501 */
 502struct rb_node *rb_first(const struct rb_root *root)
 503{
 504        struct rb_node  *n;
 505
 506        n = root->rb_node;
 507        if (!n)
 508                return NULL;
 509        while (n->rb_left)
 510                n = n->rb_left;
 511        return n;
 512}
 513EXPORT_SYMBOL(rb_first);
 514
 515struct rb_node *rb_last(const struct rb_root *root)
 516{
 517        struct rb_node  *n;
 518
 519        n = root->rb_node;
 520        if (!n)
 521                return NULL;
 522        while (n->rb_right)
 523                n = n->rb_right;
 524        return n;
 525}
 526EXPORT_SYMBOL(rb_last);
 527
 528struct rb_node *rb_next(const struct rb_node *node)
 529{
 530        struct rb_node *parent;
 531
 532        if (RB_EMPTY_NODE(node))
 533                return NULL;
 534
 535        /*
 536         * If we have a right-hand child, go down and then left as far
 537         * as we can.
 538         */
 539        if (node->rb_right) {
 540                node = node->rb_right;
 541                while (node->rb_left)
 542                        node=node->rb_left;
 543                return (struct rb_node *)node;
 544        }
 545
 546        /*
 547         * No right-hand children. Everything down and left is smaller than us,
 548         * so any 'next' node must be in the general direction of our parent.
 549         * Go up the tree; any time the ancestor is a right-hand child of its
 550         * parent, keep going up. First time it's a left-hand child of its
 551         * parent, said parent is our 'next' node.
 552         */
 553        while ((parent = rb_parent(node)) && node == parent->rb_right)
 554                node = parent;
 555
 556        return parent;
 557}
 558EXPORT_SYMBOL(rb_next);
 559
 560struct rb_node *rb_prev(const struct rb_node *node)
 561{
 562        struct rb_node *parent;
 563
 564        if (RB_EMPTY_NODE(node))
 565                return NULL;
 566
 567        /*
 568         * If we have a left-hand child, go down and then right as far
 569         * as we can.
 570         */
 571        if (node->rb_left) {
 572                node = node->rb_left;
 573                while (node->rb_right)
 574                        node=node->rb_right;
 575                return (struct rb_node *)node;
 576        }
 577
 578        /*
 579         * No left-hand children. Go up till we find an ancestor which
 580         * is a right-hand child of its parent.
 581         */
 582        while ((parent = rb_parent(node)) && node == parent->rb_left)
 583                node = parent;
 584
 585        return parent;
 586}
 587EXPORT_SYMBOL(rb_prev);
 588
 589void rb_replace_node(struct rb_node *victim, struct rb_node *new,
 590                     struct rb_root *root)
 591{
 592        struct rb_node *parent = rb_parent(victim);
 593
 594        /* Copy the pointers/colour from the victim to the replacement */
 595        *new = *victim;
 596
 597        /* Set the surrounding nodes to point to the replacement */
 598        if (victim->rb_left)
 599                rb_set_parent(victim->rb_left, new);
 600        if (victim->rb_right)
 601                rb_set_parent(victim->rb_right, new);
 602        __rb_change_child(victim, new, parent, root);
 603}
 604EXPORT_SYMBOL(rb_replace_node);
 605
 606void rb_replace_node_cached(struct rb_node *victim, struct rb_node *new,
 607                            struct rb_root_cached *root)
 608{
 609        rb_replace_node(victim, new, &root->rb_root);
 610
 611        if (root->rb_leftmost == victim)
 612                root->rb_leftmost = new;
 613}
 614EXPORT_SYMBOL(rb_replace_node_cached);
 615
 616void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new,
 617                         struct rb_root *root)
 618{
 619        struct rb_node *parent = rb_parent(victim);
 620
 621        /* Copy the pointers/colour from the victim to the replacement */
 622        *new = *victim;
 623
 624        /* Set the surrounding nodes to point to the replacement */
 625        if (victim->rb_left)
 626                rb_set_parent(victim->rb_left, new);
 627        if (victim->rb_right)
 628                rb_set_parent(victim->rb_right, new);
 629
 630        /* Set the parent's pointer to the new node last after an RCU barrier
 631         * so that the pointers onwards are seen to be set correctly when doing
 632         * an RCU walk over the tree.
 633         */
 634        __rb_change_child_rcu(victim, new, parent, root);
 635}
 636EXPORT_SYMBOL(rb_replace_node_rcu);
 637
 638static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
 639{
 640        for (;;) {
 641                if (node->rb_left)
 642                        node = node->rb_left;
 643                else if (node->rb_right)
 644                        node = node->rb_right;
 645                else
 646                        return (struct rb_node *)node;
 647        }
 648}
 649
 650struct rb_node *rb_next_postorder(const struct rb_node *node)
 651{
 652        const struct rb_node *parent;
 653        if (!node)
 654                return NULL;
 655        parent = rb_parent(node);
 656
 657        /* If we're sitting on node, we've already seen our children */
 658        if (parent && node == parent->rb_left && parent->rb_right) {
 659                /* If we are the parent's left node, go to the parent's right
 660                 * node then all the way down to the left */
 661                return rb_left_deepest_node(parent->rb_right);
 662        } else
 663                /* Otherwise we are the parent's right node, and the parent
 664                 * should be next */
 665                return (struct rb_node *)parent;
 666}
 667EXPORT_SYMBOL(rb_next_postorder);
 668
 669struct rb_node *rb_first_postorder(const struct rb_root *root)
 670{
 671        if (!root->rb_node)
 672                return NULL;
 673
 674        return rb_left_deepest_node(root->rb_node);
 675}
 676EXPORT_SYMBOL(rb_first_postorder);
 677