598 lines
16 KiB
C
598 lines
16 KiB
C
// 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 <andrea@suse.de>
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(C) 2002 David Woodhouse <dwmw2@infradead.org>
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(C) 2012 Michel Lespinasse <walken@google.com>
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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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* 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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* 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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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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/*
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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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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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/*
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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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/*
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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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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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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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if (RB_EMPTY_NODE(node))
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return NULL;
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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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* 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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return parent;
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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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if (RB_EMPTY_NODE(node))
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return NULL;
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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) {
|
|
node = node->rb_left;
|
|
while (node->rb_right)
|
|
node = node->rb_right;
|
|
return (struct rb_node *)node;
|
|
}
|
|
|
|
/*
|
|
* No left-hand children. Go up till we find an ancestor which
|
|
* is a right-hand child of its parent.
|
|
*/
|
|
while ((parent = rb_parent(node)) && node == parent->rb_left)
|
|
node = parent;
|
|
|
|
return parent;
|
|
}
|
|
|
|
void rb_replace_node(struct rb_node *victim, struct rb_node *new,
|
|
struct rb_root *root)
|
|
{
|
|
struct rb_node *parent = rb_parent(victim);
|
|
|
|
/* Copy the pointers/colour from the victim to the replacement */
|
|
*new = *victim;
|
|
|
|
/* Set the surrounding nodes to point to the replacement */
|
|
if (victim->rb_left)
|
|
rb_set_parent(victim->rb_left, new);
|
|
if (victim->rb_right)
|
|
rb_set_parent(victim->rb_right, new);
|
|
__rb_change_child(victim, new, parent, root);
|
|
}
|
|
|
|
static struct rb_node *rb_left_deepest_node(const struct rb_node *node)
|
|
{
|
|
for (;;) {
|
|
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;
|
|
}
|
|
|
|
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);
|
|
}
|