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630 lines
17 KiB
630 lines
17 KiB
// SPDX-License-Identifier: GPL-2.0-or-later |
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/* |
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Red Black Trees |
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(C) 1999 Andrea Arcangeli <[email protected]> |
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(C) 2002 David Woodhouse <[email protected]> |
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(C) 2012 Michel Lespinasse <[email protected]> |
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linux/lib/rbtree.c |
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*/ |
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#include <linux/rbtree_augmented.h> |
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#include <linux/export.h> |
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|
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/* |
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* red-black trees properties: https://en.wikipedia.org/wiki/Rbtree |
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* |
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* 1) A node is either red or black |
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* 2) The root is black |
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* 3) All leaves (NULL) are black |
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* 4) Both children of every red node are black |
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* 5) Every simple path from root to leaves contains the same number |
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* of black nodes. |
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* |
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* 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two |
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* consecutive red nodes in a path and every red node is therefore followed by |
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* a black. So if B is the number of black nodes on every simple path (as per |
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* 5), then the longest possible path due to 4 is 2B. |
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* |
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* We shall indicate color with case, where black nodes are uppercase and red |
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* nodes will be lowercase. Unknown color nodes shall be drawn as red within |
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* parentheses and have some accompanying text comment. |
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*/ |
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|
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/* |
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* Notes on lockless lookups: |
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* |
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* All stores to the tree structure (rb_left and rb_right) must be done using |
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* WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the |
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* tree structure as seen in program order. |
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* |
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* These two requirements will allow lockless iteration of the tree -- not |
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* correct iteration mind you, tree rotations are not atomic so a lookup might |
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* miss entire subtrees. |
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* |
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* But they do guarantee that any such traversal will only see valid elements |
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* and that it will indeed complete -- does not get stuck in a loop. |
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* |
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* It also guarantees that if the lookup returns an element it is the 'correct' |
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* one. But not returning an element does _NOT_ mean it's not present. |
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* |
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* NOTE: |
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* |
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* Stores to __rb_parent_color are not important for simple lookups so those |
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* are left undone as of now. Nor did I check for loops involving parent |
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* pointers. |
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*/ |
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static inline void rb_set_black(struct rb_node *rb) |
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{ |
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rb->__rb_parent_color |= RB_BLACK; |
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} |
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static inline struct rb_node *rb_red_parent(struct rb_node *red) |
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{ |
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return (struct rb_node *)red->__rb_parent_color; |
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} |
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/* |
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* Helper function for rotations: |
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* - old's parent and color get assigned to new |
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* - old gets assigned new as a parent and 'color' as a color. |
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*/ |
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static inline void |
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__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, |
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struct rb_root *root, int color) |
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{ |
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struct rb_node *parent = rb_parent(old); |
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new->__rb_parent_color = old->__rb_parent_color; |
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rb_set_parent_color(old, new, color); |
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__rb_change_child(old, new, parent, root); |
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} |
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static __always_inline void |
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__rb_insert(struct rb_node *node, struct rb_root *root, |
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void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
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{ |
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struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; |
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while (true) { |
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/* |
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* Loop invariant: node is red. |
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*/ |
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if (unlikely(!parent)) { |
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/* |
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* The inserted node is root. Either this is the |
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* first node, or we recursed at Case 1 below and |
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* are no longer violating 4). |
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*/ |
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rb_set_parent_color(node, NULL, RB_BLACK); |
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break; |
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} |
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/* |
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* If there is a black parent, we are done. |
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* Otherwise, take some corrective action as, |
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* per 4), we don't want a red root or two |
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* consecutive red nodes. |
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*/ |
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if(rb_is_black(parent)) |
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break; |
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gparent = rb_red_parent(parent); |
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|
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tmp = gparent->rb_right; |
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if (parent != tmp) { /* parent == gparent->rb_left */ |
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if (tmp && rb_is_red(tmp)) { |
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/* |
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* Case 1 - node's uncle is red (color flips). |
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* |
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* G g |
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* / \ / \ |
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* p u --> P U |
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* / / |
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* n n |
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* |
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* However, since g's parent might be red, and |
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* 4) does not allow this, we need to recurse |
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* at g. |
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*/ |
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rb_set_parent_color(tmp, gparent, RB_BLACK); |
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rb_set_parent_color(parent, gparent, RB_BLACK); |
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node = gparent; |
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parent = rb_parent(node); |
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rb_set_parent_color(node, parent, RB_RED); |
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continue; |
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} |
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tmp = parent->rb_right; |
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if (node == tmp) { |
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/* |
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* Case 2 - node's uncle is black and node is |
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* the parent's right child (left rotate at parent). |
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* |
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* G G |
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* / \ / \ |
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* p U --> n U |
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* \ / |
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* n p |
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* |
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* This still leaves us in violation of 4), the |
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* continuation into Case 3 will fix that. |
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*/ |
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tmp = node->rb_left; |
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WRITE_ONCE(parent->rb_right, tmp); |
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WRITE_ONCE(node->rb_left, parent); |
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if (tmp) |
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rb_set_parent_color(tmp, parent, |
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RB_BLACK); |
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rb_set_parent_color(parent, node, RB_RED); |
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augment_rotate(parent, node); |
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parent = node; |
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tmp = node->rb_right; |
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} |
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/* |
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* Case 3 - node's uncle is black and node is |
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* the parent's left child (right rotate at gparent). |
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* |
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* G P |
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* / \ / \ |
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* p U --> n g |
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* / \ |
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* n U |
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*/ |
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WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */ |
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WRITE_ONCE(parent->rb_right, gparent); |
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if (tmp) |
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rb_set_parent_color(tmp, gparent, RB_BLACK); |
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__rb_rotate_set_parents(gparent, parent, root, RB_RED); |
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augment_rotate(gparent, parent); |
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break; |
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} else { |
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tmp = gparent->rb_left; |
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if (tmp && rb_is_red(tmp)) { |
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/* Case 1 - color flips */ |
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rb_set_parent_color(tmp, gparent, RB_BLACK); |
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rb_set_parent_color(parent, gparent, RB_BLACK); |
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node = gparent; |
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parent = rb_parent(node); |
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rb_set_parent_color(node, parent, RB_RED); |
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continue; |
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} |
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tmp = parent->rb_left; |
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if (node == tmp) { |
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/* Case 2 - right rotate at parent */ |
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tmp = node->rb_right; |
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WRITE_ONCE(parent->rb_left, tmp); |
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WRITE_ONCE(node->rb_right, parent); |
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if (tmp) |
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rb_set_parent_color(tmp, parent, |
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RB_BLACK); |
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rb_set_parent_color(parent, node, RB_RED); |
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augment_rotate(parent, node); |
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parent = node; |
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tmp = node->rb_left; |
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} |
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/* Case 3 - left rotate at gparent */ |
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WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */ |
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WRITE_ONCE(parent->rb_left, gparent); |
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if (tmp) |
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rb_set_parent_color(tmp, gparent, RB_BLACK); |
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__rb_rotate_set_parents(gparent, parent, root, RB_RED); |
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augment_rotate(gparent, parent); |
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break; |
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} |
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} |
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} |
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/* |
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* Inline version for rb_erase() use - we want to be able to inline |
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* and eliminate the dummy_rotate callback there |
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*/ |
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static __always_inline void |
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____rb_erase_color(struct rb_node *parent, struct rb_root *root, |
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void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
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{ |
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struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; |
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while (true) { |
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/* |
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* Loop invariants: |
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* - node is black (or NULL on first iteration) |
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* - node is not the root (parent is not NULL) |
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* - All leaf paths going through parent and node have a |
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* black node count that is 1 lower than other leaf paths. |
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*/ |
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sibling = parent->rb_right; |
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if (node != sibling) { /* node == parent->rb_left */ |
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if (rb_is_red(sibling)) { |
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/* |
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* Case 1 - left rotate at parent |
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* |
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* P S |
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* / \ / \ |
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* N s --> p Sr |
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* / \ / \ |
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* Sl Sr N Sl |
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*/ |
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tmp1 = sibling->rb_left; |
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WRITE_ONCE(parent->rb_right, tmp1); |
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WRITE_ONCE(sibling->rb_left, parent); |
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rb_set_parent_color(tmp1, parent, RB_BLACK); |
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__rb_rotate_set_parents(parent, sibling, root, |
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RB_RED); |
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augment_rotate(parent, sibling); |
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sibling = tmp1; |
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} |
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tmp1 = sibling->rb_right; |
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if (!tmp1 || rb_is_black(tmp1)) { |
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tmp2 = sibling->rb_left; |
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if (!tmp2 || rb_is_black(tmp2)) { |
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/* |
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* Case 2 - sibling color flip |
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* (p could be either color here) |
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* |
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* (p) (p) |
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* / \ / \ |
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* N S --> N s |
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* / \ / \ |
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* Sl Sr Sl Sr |
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* |
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* This leaves us violating 5) which |
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* can be fixed by flipping p to black |
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* if it was red, or by recursing at p. |
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* p is red when coming from Case 1. |
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*/ |
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rb_set_parent_color(sibling, parent, |
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RB_RED); |
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if (rb_is_red(parent)) |
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rb_set_black(parent); |
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else { |
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node = parent; |
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parent = rb_parent(node); |
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if (parent) |
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continue; |
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} |
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break; |
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} |
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/* |
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* Case 3 - right rotate at sibling |
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* (p could be either color here) |
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* |
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* (p) (p) |
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* / \ / \ |
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* N S --> N sl |
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* / \ \ |
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* sl Sr S |
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* \ |
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* Sr |
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* |
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* Note: p might be red, and then both |
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* p and sl are red after rotation(which |
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* breaks property 4). This is fixed in |
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* Case 4 (in __rb_rotate_set_parents() |
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* which set sl the color of p |
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* and set p RB_BLACK) |
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* |
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* (p) (sl) |
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* / \ / \ |
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* N sl --> P S |
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* \ / \ |
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* S N Sr |
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* \ |
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* Sr |
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*/ |
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tmp1 = tmp2->rb_right; |
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WRITE_ONCE(sibling->rb_left, tmp1); |
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WRITE_ONCE(tmp2->rb_right, sibling); |
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WRITE_ONCE(parent->rb_right, tmp2); |
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if (tmp1) |
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rb_set_parent_color(tmp1, sibling, |
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RB_BLACK); |
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augment_rotate(sibling, tmp2); |
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tmp1 = sibling; |
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sibling = tmp2; |
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} |
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/* |
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* Case 4 - left rotate at parent + color flips |
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* (p and sl could be either color here. |
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* After rotation, p becomes black, s acquires |
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* p's color, and sl keeps its color) |
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* |
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* (p) (s) |
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* / \ / \ |
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* N S --> P Sr |
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* / \ / \ |
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* (sl) sr N (sl) |
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*/ |
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tmp2 = sibling->rb_left; |
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WRITE_ONCE(parent->rb_right, tmp2); |
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WRITE_ONCE(sibling->rb_left, parent); |
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rb_set_parent_color(tmp1, sibling, RB_BLACK); |
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if (tmp2) |
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rb_set_parent(tmp2, parent); |
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__rb_rotate_set_parents(parent, sibling, root, |
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RB_BLACK); |
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augment_rotate(parent, sibling); |
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break; |
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} else { |
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sibling = parent->rb_left; |
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if (rb_is_red(sibling)) { |
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/* Case 1 - right rotate at parent */ |
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tmp1 = sibling->rb_right; |
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WRITE_ONCE(parent->rb_left, tmp1); |
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WRITE_ONCE(sibling->rb_right, parent); |
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rb_set_parent_color(tmp1, parent, RB_BLACK); |
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__rb_rotate_set_parents(parent, sibling, root, |
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RB_RED); |
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augment_rotate(parent, sibling); |
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sibling = tmp1; |
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} |
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tmp1 = sibling->rb_left; |
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if (!tmp1 || rb_is_black(tmp1)) { |
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tmp2 = sibling->rb_right; |
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if (!tmp2 || rb_is_black(tmp2)) { |
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/* Case 2 - sibling color flip */ |
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rb_set_parent_color(sibling, parent, |
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RB_RED); |
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if (rb_is_red(parent)) |
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rb_set_black(parent); |
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else { |
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node = parent; |
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parent = rb_parent(node); |
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if (parent) |
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continue; |
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} |
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break; |
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} |
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/* Case 3 - left rotate at sibling */ |
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tmp1 = tmp2->rb_left; |
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WRITE_ONCE(sibling->rb_right, tmp1); |
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WRITE_ONCE(tmp2->rb_left, sibling); |
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WRITE_ONCE(parent->rb_left, tmp2); |
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if (tmp1) |
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rb_set_parent_color(tmp1, sibling, |
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RB_BLACK); |
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augment_rotate(sibling, tmp2); |
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tmp1 = sibling; |
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sibling = tmp2; |
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} |
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/* Case 4 - right rotate at parent + color flips */ |
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tmp2 = sibling->rb_right; |
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WRITE_ONCE(parent->rb_left, tmp2); |
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WRITE_ONCE(sibling->rb_right, parent); |
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rb_set_parent_color(tmp1, sibling, RB_BLACK); |
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if (tmp2) |
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rb_set_parent(tmp2, parent); |
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__rb_rotate_set_parents(parent, sibling, root, |
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RB_BLACK); |
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augment_rotate(parent, sibling); |
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break; |
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} |
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} |
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} |
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/* Non-inline version for rb_erase_augmented() use */ |
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void __rb_erase_color(struct rb_node *parent, struct rb_root *root, |
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void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
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{ |
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____rb_erase_color(parent, root, augment_rotate); |
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} |
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EXPORT_SYMBOL(__rb_erase_color); |
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|
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/* |
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* Non-augmented rbtree manipulation functions. |
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* |
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* We use dummy augmented callbacks here, and have the compiler optimize them |
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* out of the rb_insert_color() and rb_erase() function definitions. |
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*/ |
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static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} |
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static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} |
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static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} |
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static const struct rb_augment_callbacks dummy_callbacks = { |
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.propagate = dummy_propagate, |
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.copy = dummy_copy, |
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.rotate = dummy_rotate |
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}; |
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void rb_insert_color(struct rb_node *node, struct rb_root *root) |
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{ |
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__rb_insert(node, root, dummy_rotate); |
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} |
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EXPORT_SYMBOL(rb_insert_color); |
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void rb_erase(struct rb_node *node, struct rb_root *root) |
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{ |
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struct rb_node *rebalance; |
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rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); |
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if (rebalance) |
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____rb_erase_color(rebalance, root, dummy_rotate); |
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} |
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EXPORT_SYMBOL(rb_erase); |
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|
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/* |
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* Augmented rbtree manipulation functions. |
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* |
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* This instantiates the same __always_inline functions as in the non-augmented |
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* case, but this time with user-defined callbacks. |
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*/ |
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void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, |
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void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) |
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{ |
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__rb_insert(node, root, augment_rotate); |
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} |
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EXPORT_SYMBOL(__rb_insert_augmented); |
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|
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/* |
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* This function returns the first node (in sort order) of the tree. |
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*/ |
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struct rb_node *rb_first(const struct rb_root *root) |
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{ |
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struct rb_node *n; |
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n = root->rb_node; |
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if (!n) |
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return NULL; |
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while (n->rb_left) |
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n = n->rb_left; |
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return n; |
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} |
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EXPORT_SYMBOL(rb_first); |
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struct rb_node *rb_last(const struct rb_root *root) |
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{ |
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struct rb_node *n; |
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n = root->rb_node; |
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if (!n) |
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return NULL; |
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while (n->rb_right) |
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n = n->rb_right; |
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return n; |
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} |
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EXPORT_SYMBOL(rb_last); |
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struct rb_node *rb_next(const struct rb_node *node) |
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{ |
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struct rb_node *parent; |
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|
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if (RB_EMPTY_NODE(node)) |
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return NULL; |
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|
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/* |
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* If we have a right-hand child, go down and then left as far |
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* as we can. |
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*/ |
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if (node->rb_right) { |
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node = node->rb_right; |
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while (node->rb_left) |
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node = node->rb_left; |
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return (struct rb_node *)node; |
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} |
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|
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/* |
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* No right-hand children. Everything down and left is smaller than us, |
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* so any 'next' node must be in the general direction of our parent. |
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* Go up the tree; any time the ancestor is a right-hand child of its |
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* parent, keep going up. First time it's a left-hand child of its |
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* parent, said parent is our 'next' node. |
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*/ |
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while ((parent = rb_parent(node)) && node == parent->rb_right) |
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node = parent; |
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|
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return parent; |
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} |
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EXPORT_SYMBOL(rb_next); |
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|
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struct rb_node *rb_prev(const struct rb_node *node) |
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{ |
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struct rb_node *parent; |
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|
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if (RB_EMPTY_NODE(node)) |
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return NULL; |
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|
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/* |
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* If we have a left-hand child, go down and then right as far |
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* as we can. |
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*/ |
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if (node->rb_left) { |
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node = node->rb_left; |
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while (node->rb_right) |
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node = node->rb_right; |
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return (struct rb_node *)node; |
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} |
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|
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/* |
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* No left-hand children. Go up till we find an ancestor which |
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* is a right-hand child of its parent. |
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*/ |
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while ((parent = rb_parent(node)) && node == parent->rb_left) |
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node = parent; |
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|
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return parent; |
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} |
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EXPORT_SYMBOL(rb_prev); |
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|
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void rb_replace_node(struct rb_node *victim, struct rb_node *new, |
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struct rb_root *root) |
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{ |
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struct rb_node *parent = rb_parent(victim); |
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|
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/* Copy the pointers/colour from the victim to the replacement */ |
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*new = *victim; |
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|
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/* Set the surrounding nodes to point to the replacement */ |
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if (victim->rb_left) |
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rb_set_parent(victim->rb_left, new); |
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if (victim->rb_right) |
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rb_set_parent(victim->rb_right, new); |
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__rb_change_child(victim, new, parent, root); |
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} |
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EXPORT_SYMBOL(rb_replace_node); |
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|
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void rb_replace_node_rcu(struct rb_node *victim, struct rb_node *new, |
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struct rb_root *root) |
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{ |
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struct rb_node *parent = rb_parent(victim); |
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|
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/* Copy the pointers/colour from the victim to the replacement */ |
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*new = *victim; |
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|
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/* Set the surrounding nodes to point to the replacement */ |
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if (victim->rb_left) |
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rb_set_parent(victim->rb_left, new); |
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if (victim->rb_right) |
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rb_set_parent(victim->rb_right, new); |
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|
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/* Set the parent's pointer to the new node last after an RCU barrier |
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* so that the pointers onwards are seen to be set correctly when doing |
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* an RCU walk over the tree. |
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*/ |
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__rb_change_child_rcu(victim, new, parent, root); |
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} |
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EXPORT_SYMBOL(rb_replace_node_rcu); |
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|
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static struct rb_node *rb_left_deepest_node(const struct rb_node *node) |
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{ |
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for (;;) { |
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if (node->rb_left) |
|
node = node->rb_left; |
|
else if (node->rb_right) |
|
node = node->rb_right; |
|
else |
|
return (struct rb_node *)node; |
|
} |
|
} |
|
|
|
struct rb_node *rb_next_postorder(const struct rb_node *node) |
|
{ |
|
const struct rb_node *parent; |
|
if (!node) |
|
return NULL; |
|
parent = rb_parent(node); |
|
|
|
/* If we're sitting on node, we've already seen our children */ |
|
if (parent && node == parent->rb_left && parent->rb_right) { |
|
/* If we are the parent's left node, go to the parent's right |
|
* node then all the way down to the left */ |
|
return rb_left_deepest_node(parent->rb_right); |
|
} else |
|
/* Otherwise we are the parent's right node, and the parent |
|
* should be next */ |
|
return (struct rb_node *)parent; |
|
} |
|
EXPORT_SYMBOL(rb_next_postorder); |
|
|
|
struct rb_node *rb_first_postorder(const struct rb_root *root) |
|
{ |
|
if (!root->rb_node) |
|
return NULL; |
|
|
|
return rb_left_deepest_node(root->rb_node); |
|
} |
|
EXPORT_SYMBOL(rb_first_postorder);
|
|
|