883 lines
28 KiB
C
883 lines
28 KiB
C
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/* SPDX-License-Identifier: GPL-2.0-or-later */
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#include "qemu/osdep.h"
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#include "qemu/interval-tree.h"
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#include "qemu/atomic.h"
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/*
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* Red Black Trees.
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*
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* For now, don't expose Linux Red-Black Trees separately, but retain the
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* separate type definitions to keep the implementation sane, and allow
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* the possibility of separating them later.
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*
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* Derived from include/linux/rbtree_augmented.h and its dependencies.
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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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* 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 [qatomic_set for QEMU]. And we must not inadvertently cause
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* (temporary) loops in the 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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typedef enum RBColor
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{
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RB_RED,
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RB_BLACK,
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} RBColor;
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typedef struct RBAugmentCallbacks {
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void (*propagate)(RBNode *node, RBNode *stop);
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void (*copy)(RBNode *old, RBNode *new);
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void (*rotate)(RBNode *old, RBNode *new);
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} RBAugmentCallbacks;
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static inline RBNode *rb_parent(const RBNode *n)
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{
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return (RBNode *)(n->rb_parent_color & ~1);
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}
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static inline RBNode *rb_red_parent(const RBNode *n)
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{
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return (RBNode *)n->rb_parent_color;
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}
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static inline RBColor pc_color(uintptr_t pc)
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{
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return (RBColor)(pc & 1);
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}
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static inline bool pc_is_red(uintptr_t pc)
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{
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return pc_color(pc) == RB_RED;
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}
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static inline bool pc_is_black(uintptr_t pc)
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{
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return !pc_is_red(pc);
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}
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static inline RBColor rb_color(const RBNode *n)
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{
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return pc_color(n->rb_parent_color);
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}
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static inline bool rb_is_red(const RBNode *n)
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{
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return pc_is_red(n->rb_parent_color);
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}
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static inline bool rb_is_black(const RBNode *n)
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{
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return pc_is_black(n->rb_parent_color);
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}
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static inline void rb_set_black(RBNode *n)
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{
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n->rb_parent_color |= RB_BLACK;
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}
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static inline void rb_set_parent_color(RBNode *n, RBNode *p, RBColor color)
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{
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n->rb_parent_color = (uintptr_t)p | color;
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}
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static inline void rb_set_parent(RBNode *n, RBNode *p)
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{
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rb_set_parent_color(n, p, rb_color(n));
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}
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static inline void rb_link_node(RBNode *node, RBNode *parent, RBNode **rb_link)
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{
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node->rb_parent_color = (uintptr_t)parent;
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node->rb_left = node->rb_right = NULL;
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qatomic_set(rb_link, node);
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}
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static RBNode *rb_next(RBNode *node)
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{
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RBNode *parent;
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/* OMIT: if empty node, return null. */
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/*
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* If we have a right-hand child, go down and then left as far 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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}
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return 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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}
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return parent;
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}
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static inline void rb_change_child(RBNode *old, RBNode *new,
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RBNode *parent, RBRoot *root)
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{
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if (!parent) {
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qatomic_set(&root->rb_node, new);
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} else if (parent->rb_left == old) {
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qatomic_set(&parent->rb_left, new);
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} else {
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qatomic_set(&parent->rb_right, new);
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}
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}
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static inline void rb_rotate_set_parents(RBNode *old, RBNode *new,
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RBRoot *root, RBColor color)
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{
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RBNode *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 void rb_insert_augmented(RBNode *node, RBRoot *root,
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const RBAugmentCallbacks *augment)
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{
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RBNode *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 first node, or
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* we recursed at Case 1 below and 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. Otherwise, take some
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* corrective action as, 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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}
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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 4) does not
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* allow this, we need to recurse 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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qatomic_set(&parent->rb_right, tmp);
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qatomic_set(&node->rb_left, parent);
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if (tmp) {
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rb_set_parent_color(tmp, parent, RB_BLACK);
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}
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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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qatomic_set(&gparent->rb_left, tmp); /* == parent->rb_right */
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qatomic_set(&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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}
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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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qatomic_set(&parent->rb_left, tmp);
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qatomic_set(&node->rb_right, parent);
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if (tmp) {
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rb_set_parent_color(tmp, parent, RB_BLACK);
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}
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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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qatomic_set(&gparent->rb_right, tmp); /* == parent->rb_left */
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qatomic_set(&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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}
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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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static void rb_insert_augmented_cached(RBNode *node,
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RBRootLeftCached *root, bool newleft,
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const RBAugmentCallbacks *augment)
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{
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if (newleft) {
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root->rb_leftmost = node;
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}
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rb_insert_augmented(node, &root->rb_root, augment);
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}
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static void rb_erase_color(RBNode *parent, RBRoot *root,
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const RBAugmentCallbacks *augment)
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{
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RBNode *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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qatomic_set(&parent->rb_right, tmp1);
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qatomic_set(&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, 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.
|
||
|
|
* p is red when coming from Case 1.
|
||
|
|
*/
|
||
|
|
rb_set_parent_color(sibling, parent, RB_RED);
|
||
|
|
if (rb_is_red(parent)) {
|
||
|
|
rb_set_black(parent);
|
||
|
|
} else {
|
||
|
|
node = parent;
|
||
|
|
parent = rb_parent(node);
|
||
|
|
if (parent) {
|
||
|
|
continue;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
/*
|
||
|
|
* Case 3 - right rotate at sibling
|
||
|
|
* (p could be either color here)
|
||
|
|
*
|
||
|
|
* (p) (p)
|
||
|
|
* / \ / \
|
||
|
|
* N S --> N sl
|
||
|
|
* / \ \
|
||
|
|
* sl Sr S
|
||
|
|
* \
|
||
|
|
* Sr
|
||
|
|
*
|
||
|
|
* Note: p might be red, and then bot
|
||
|
|
* p and sl are red after rotation (which
|
||
|
|
* breaks property 4). This is fixed in
|
||
|
|
* Case 4 (in rb_rotate_set_parents()
|
||
|
|
* which set sl the color of p
|
||
|
|
* and set p RB_BLACK)
|
||
|
|
*
|
||
|
|
* (p) (sl)
|
||
|
|
* / \ / \
|
||
|
|
* N sl --> P S
|
||
|
|
* \ / \
|
||
|
|
* S N Sr
|
||
|
|
* \
|
||
|
|
* Sr
|
||
|
|
*/
|
||
|
|
tmp1 = tmp2->rb_right;
|
||
|
|
qatomic_set(&sibling->rb_left, tmp1);
|
||
|
|
qatomic_set(&tmp2->rb_right, sibling);
|
||
|
|
qatomic_set(&parent->rb_right, tmp2);
|
||
|
|
if (tmp1) {
|
||
|
|
rb_set_parent_color(tmp1, sibling, RB_BLACK);
|
||
|
|
}
|
||
|
|
augment->rotate(sibling, tmp2);
|
||
|
|
tmp1 = sibling;
|
||
|
|
sibling = tmp2;
|
||
|
|
}
|
||
|
|
/*
|
||
|
|
* Case 4 - left rotate at parent + color flips
|
||
|
|
* (p and sl could be either color here.
|
||
|
|
* After rotation, p becomes black, s acquires
|
||
|
|
* p's color, and sl keeps its color)
|
||
|
|
*
|
||
|
|
* (p) (s)
|
||
|
|
* / \ / \
|
||
|
|
* N S --> P Sr
|
||
|
|
* / \ / \
|
||
|
|
* (sl) sr N (sl)
|
||
|
|
*/
|
||
|
|
tmp2 = sibling->rb_left;
|
||
|
|
qatomic_set(&parent->rb_right, tmp2);
|
||
|
|
qatomic_set(&sibling->rb_left, parent);
|
||
|
|
rb_set_parent_color(tmp1, sibling, RB_BLACK);
|
||
|
|
if (tmp2) {
|
||
|
|
rb_set_parent(tmp2, parent);
|
||
|
|
}
|
||
|
|
rb_rotate_set_parents(parent, sibling, root, RB_BLACK);
|
||
|
|
augment->rotate(parent, sibling);
|
||
|
|
break;
|
||
|
|
} else {
|
||
|
|
sibling = parent->rb_left;
|
||
|
|
if (rb_is_red(sibling)) {
|
||
|
|
/* Case 1 - right rotate at parent */
|
||
|
|
tmp1 = sibling->rb_right;
|
||
|
|
qatomic_set(&parent->rb_left, tmp1);
|
||
|
|
qatomic_set(&sibling->rb_right, parent);
|
||
|
|
rb_set_parent_color(tmp1, parent, RB_BLACK);
|
||
|
|
rb_rotate_set_parents(parent, sibling, root, RB_RED);
|
||
|
|
augment->rotate(parent, sibling);
|
||
|
|
sibling = tmp1;
|
||
|
|
}
|
||
|
|
tmp1 = sibling->rb_left;
|
||
|
|
if (!tmp1 || rb_is_black(tmp1)) {
|
||
|
|
tmp2 = sibling->rb_right;
|
||
|
|
if (!tmp2 || rb_is_black(tmp2)) {
|
||
|
|
/* Case 2 - sibling color flip */
|
||
|
|
rb_set_parent_color(sibling, parent, RB_RED);
|
||
|
|
if (rb_is_red(parent)) {
|
||
|
|
rb_set_black(parent);
|
||
|
|
} else {
|
||
|
|
node = parent;
|
||
|
|
parent = rb_parent(node);
|
||
|
|
if (parent) {
|
||
|
|
continue;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
/* Case 3 - left rotate at sibling */
|
||
|
|
tmp1 = tmp2->rb_left;
|
||
|
|
qatomic_set(&sibling->rb_right, tmp1);
|
||
|
|
qatomic_set(&tmp2->rb_left, sibling);
|
||
|
|
qatomic_set(&parent->rb_left, tmp2);
|
||
|
|
if (tmp1) {
|
||
|
|
rb_set_parent_color(tmp1, sibling, RB_BLACK);
|
||
|
|
}
|
||
|
|
augment->rotate(sibling, tmp2);
|
||
|
|
tmp1 = sibling;
|
||
|
|
sibling = tmp2;
|
||
|
|
}
|
||
|
|
/* Case 4 - right rotate at parent + color flips */
|
||
|
|
tmp2 = sibling->rb_right;
|
||
|
|
qatomic_set(&parent->rb_left, tmp2);
|
||
|
|
qatomic_set(&sibling->rb_right, parent);
|
||
|
|
rb_set_parent_color(tmp1, sibling, RB_BLACK);
|
||
|
|
if (tmp2) {
|
||
|
|
rb_set_parent(tmp2, parent);
|
||
|
|
}
|
||
|
|
rb_rotate_set_parents(parent, sibling, root, RB_BLACK);
|
||
|
|
augment->rotate(parent, sibling);
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
static void rb_erase_augmented(RBNode *node, RBRoot *root,
|
||
|
|
const RBAugmentCallbacks *augment)
|
||
|
|
{
|
||
|
|
RBNode *child = node->rb_right;
|
||
|
|
RBNode *tmp = node->rb_left;
|
||
|
|
RBNode *parent, *rebalance;
|
||
|
|
uintptr_t pc;
|
||
|
|
|
||
|
|
if (!tmp) {
|
||
|
|
/*
|
||
|
|
* Case 1: node to erase has no more than 1 child (easy!)
|
||
|
|
*
|
||
|
|
* Note that if there is one child it must be red due to 5)
|
||
|
|
* and node must be black due to 4). We adjust colors locally
|
||
|
|
* so as to bypass rb_erase_color() later on.
|
||
|
|
*/
|
||
|
|
pc = node->rb_parent_color;
|
||
|
|
parent = rb_parent(node);
|
||
|
|
rb_change_child(node, child, parent, root);
|
||
|
|
if (child) {
|
||
|
|
child->rb_parent_color = pc;
|
||
|
|
rebalance = NULL;
|
||
|
|
} else {
|
||
|
|
rebalance = pc_is_black(pc) ? parent : NULL;
|
||
|
|
}
|
||
|
|
tmp = parent;
|
||
|
|
} else if (!child) {
|
||
|
|
/* Still case 1, but this time the child is node->rb_left */
|
||
|
|
pc = node->rb_parent_color;
|
||
|
|
parent = rb_parent(node);
|
||
|
|
tmp->rb_parent_color = pc;
|
||
|
|
rb_change_child(node, tmp, parent, root);
|
||
|
|
rebalance = NULL;
|
||
|
|
tmp = parent;
|
||
|
|
} else {
|
||
|
|
RBNode *successor = child, *child2;
|
||
|
|
tmp = child->rb_left;
|
||
|
|
if (!tmp) {
|
||
|
|
/*
|
||
|
|
* Case 2: node's successor is its right child
|
||
|
|
*
|
||
|
|
* (n) (s)
|
||
|
|
* / \ / \
|
||
|
|
* (x) (s) -> (x) (c)
|
||
|
|
* \
|
||
|
|
* (c)
|
||
|
|
*/
|
||
|
|
parent = successor;
|
||
|
|
child2 = successor->rb_right;
|
||
|
|
|
||
|
|
augment->copy(node, successor);
|
||
|
|
} else {
|
||
|
|
/*
|
||
|
|
* Case 3: node's successor is leftmost under
|
||
|
|
* node's right child subtree
|
||
|
|
*
|
||
|
|
* (n) (s)
|
||
|
|
* / \ / \
|
||
|
|
* (x) (y) -> (x) (y)
|
||
|
|
* / /
|
||
|
|
* (p) (p)
|
||
|
|
* / /
|
||
|
|
* (s) (c)
|
||
|
|
* \
|
||
|
|
* (c)
|
||
|
|
*/
|
||
|
|
do {
|
||
|
|
parent = successor;
|
||
|
|
successor = tmp;
|
||
|
|
tmp = tmp->rb_left;
|
||
|
|
} while (tmp);
|
||
|
|
child2 = successor->rb_right;
|
||
|
|
qatomic_set(&parent->rb_left, child2);
|
||
|
|
qatomic_set(&successor->rb_right, child);
|
||
|
|
rb_set_parent(child, successor);
|
||
|
|
|
||
|
|
augment->copy(node, successor);
|
||
|
|
augment->propagate(parent, successor);
|
||
|
|
}
|
||
|
|
|
||
|
|
tmp = node->rb_left;
|
||
|
|
qatomic_set(&successor->rb_left, tmp);
|
||
|
|
rb_set_parent(tmp, successor);
|
||
|
|
|
||
|
|
pc = node->rb_parent_color;
|
||
|
|
tmp = rb_parent(node);
|
||
|
|
rb_change_child(node, successor, tmp, root);
|
||
|
|
|
||
|
|
if (child2) {
|
||
|
|
rb_set_parent_color(child2, parent, RB_BLACK);
|
||
|
|
rebalance = NULL;
|
||
|
|
} else {
|
||
|
|
rebalance = rb_is_black(successor) ? parent : NULL;
|
||
|
|
}
|
||
|
|
successor->rb_parent_color = pc;
|
||
|
|
tmp = successor;
|
||
|
|
}
|
||
|
|
|
||
|
|
augment->propagate(tmp, NULL);
|
||
|
|
|
||
|
|
if (rebalance) {
|
||
|
|
rb_erase_color(rebalance, root, augment);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
static void rb_erase_augmented_cached(RBNode *node, RBRootLeftCached *root,
|
||
|
|
const RBAugmentCallbacks *augment)
|
||
|
|
{
|
||
|
|
if (root->rb_leftmost == node) {
|
||
|
|
root->rb_leftmost = rb_next(node);
|
||
|
|
}
|
||
|
|
rb_erase_augmented(node, &root->rb_root, augment);
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
* Interval trees.
|
||
|
|
*
|
||
|
|
* Derived from lib/interval_tree.c and its dependencies,
|
||
|
|
* especially include/linux/interval_tree_generic.h.
|
||
|
|
*/
|
||
|
|
|
||
|
|
#define rb_to_itree(N) container_of(N, IntervalTreeNode, rb)
|
||
|
|
|
||
|
|
static bool interval_tree_compute_max(IntervalTreeNode *node, bool exit)
|
||
|
|
{
|
||
|
|
IntervalTreeNode *child;
|
||
|
|
uint64_t max = node->last;
|
||
|
|
|
||
|
|
if (node->rb.rb_left) {
|
||
|
|
child = rb_to_itree(node->rb.rb_left);
|
||
|
|
if (child->subtree_last > max) {
|
||
|
|
max = child->subtree_last;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (node->rb.rb_right) {
|
||
|
|
child = rb_to_itree(node->rb.rb_right);
|
||
|
|
if (child->subtree_last > max) {
|
||
|
|
max = child->subtree_last;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (exit && node->subtree_last == max) {
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
node->subtree_last = max;
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
static void interval_tree_propagate(RBNode *rb, RBNode *stop)
|
||
|
|
{
|
||
|
|
while (rb != stop) {
|
||
|
|
IntervalTreeNode *node = rb_to_itree(rb);
|
||
|
|
if (interval_tree_compute_max(node, true)) {
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
rb = rb_parent(&node->rb);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
static void interval_tree_copy(RBNode *rb_old, RBNode *rb_new)
|
||
|
|
{
|
||
|
|
IntervalTreeNode *old = rb_to_itree(rb_old);
|
||
|
|
IntervalTreeNode *new = rb_to_itree(rb_new);
|
||
|
|
|
||
|
|
new->subtree_last = old->subtree_last;
|
||
|
|
}
|
||
|
|
|
||
|
|
static void interval_tree_rotate(RBNode *rb_old, RBNode *rb_new)
|
||
|
|
{
|
||
|
|
IntervalTreeNode *old = rb_to_itree(rb_old);
|
||
|
|
IntervalTreeNode *new = rb_to_itree(rb_new);
|
||
|
|
|
||
|
|
new->subtree_last = old->subtree_last;
|
||
|
|
interval_tree_compute_max(old, false);
|
||
|
|
}
|
||
|
|
|
||
|
|
static const RBAugmentCallbacks interval_tree_augment = {
|
||
|
|
.propagate = interval_tree_propagate,
|
||
|
|
.copy = interval_tree_copy,
|
||
|
|
.rotate = interval_tree_rotate,
|
||
|
|
};
|
||
|
|
|
||
|
|
/* Insert / remove interval nodes from the tree */
|
||
|
|
void interval_tree_insert(IntervalTreeNode *node, IntervalTreeRoot *root)
|
||
|
|
{
|
||
|
|
RBNode **link = &root->rb_root.rb_node, *rb_parent = NULL;
|
||
|
|
uint64_t start = node->start, last = node->last;
|
||
|
|
IntervalTreeNode *parent;
|
||
|
|
bool leftmost = true;
|
||
|
|
|
||
|
|
while (*link) {
|
||
|
|
rb_parent = *link;
|
||
|
|
parent = rb_to_itree(rb_parent);
|
||
|
|
|
||
|
|
if (parent->subtree_last < last) {
|
||
|
|
parent->subtree_last = last;
|
||
|
|
}
|
||
|
|
if (start < parent->start) {
|
||
|
|
link = &parent->rb.rb_left;
|
||
|
|
} else {
|
||
|
|
link = &parent->rb.rb_right;
|
||
|
|
leftmost = false;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
node->subtree_last = last;
|
||
|
|
rb_link_node(&node->rb, rb_parent, link);
|
||
|
|
rb_insert_augmented_cached(&node->rb, root, leftmost,
|
||
|
|
&interval_tree_augment);
|
||
|
|
}
|
||
|
|
|
||
|
|
void interval_tree_remove(IntervalTreeNode *node, IntervalTreeRoot *root)
|
||
|
|
{
|
||
|
|
rb_erase_augmented_cached(&node->rb, root, &interval_tree_augment);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
* Iterate over intervals intersecting [start;last]
|
||
|
|
*
|
||
|
|
* Note that a node's interval intersects [start;last] iff:
|
||
|
|
* Cond1: node->start <= last
|
||
|
|
* and
|
||
|
|
* Cond2: start <= node->last
|
||
|
|
*/
|
||
|
|
|
||
|
|
static IntervalTreeNode *interval_tree_subtree_search(IntervalTreeNode *node,
|
||
|
|
uint64_t start,
|
||
|
|
uint64_t last)
|
||
|
|
{
|
||
|
|
while (true) {
|
||
|
|
/*
|
||
|
|
* Loop invariant: start <= node->subtree_last
|
||
|
|
* (Cond2 is satisfied by one of the subtree nodes)
|
||
|
|
*/
|
||
|
|
if (node->rb.rb_left) {
|
||
|
|
IntervalTreeNode *left = rb_to_itree(node->rb.rb_left);
|
||
|
|
|
||
|
|
if (start <= left->subtree_last) {
|
||
|
|
/*
|
||
|
|
* Some nodes in left subtree satisfy Cond2.
|
||
|
|
* Iterate to find the leftmost such node N.
|
||
|
|
* If it also satisfies Cond1, that's the
|
||
|
|
* match we are looking for. Otherwise, there
|
||
|
|
* is no matching interval as nodes to the
|
||
|
|
* right of N can't satisfy Cond1 either.
|
||
|
|
*/
|
||
|
|
node = left;
|
||
|
|
continue;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
if (node->start <= last) { /* Cond1 */
|
||
|
|
if (start <= node->last) { /* Cond2 */
|
||
|
|
return node; /* node is leftmost match */
|
||
|
|
}
|
||
|
|
if (node->rb.rb_right) {
|
||
|
|
node = rb_to_itree(node->rb.rb_right);
|
||
|
|
if (start <= node->subtree_last) {
|
||
|
|
continue;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
return NULL; /* no match */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
IntervalTreeNode *interval_tree_iter_first(IntervalTreeRoot *root,
|
||
|
|
uint64_t start, uint64_t last)
|
||
|
|
{
|
||
|
|
IntervalTreeNode *node, *leftmost;
|
||
|
|
|
||
|
|
if (!root->rb_root.rb_node) {
|
||
|
|
return NULL;
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
* Fastpath range intersection/overlap between A: [a0, a1] and
|
||
|
|
* B: [b0, b1] is given by:
|
||
|
|
*
|
||
|
|
* a0 <= b1 && b0 <= a1
|
||
|
|
*
|
||
|
|
* ... where A holds the lock range and B holds the smallest
|
||
|
|
* 'start' and largest 'last' in the tree. For the later, we
|
||
|
|
* rely on the root node, which by augmented interval tree
|
||
|
|
* property, holds the largest value in its last-in-subtree.
|
||
|
|
* This allows mitigating some of the tree walk overhead for
|
||
|
|
* for non-intersecting ranges, maintained and consulted in O(1).
|
||
|
|
*/
|
||
|
|
node = rb_to_itree(root->rb_root.rb_node);
|
||
|
|
if (node->subtree_last < start) {
|
||
|
|
return NULL;
|
||
|
|
}
|
||
|
|
|
||
|
|
leftmost = rb_to_itree(root->rb_leftmost);
|
||
|
|
if (leftmost->start > last) {
|
||
|
|
return NULL;
|
||
|
|
}
|
||
|
|
|
||
|
|
return interval_tree_subtree_search(node, start, last);
|
||
|
|
}
|
||
|
|
|
||
|
|
IntervalTreeNode *interval_tree_iter_next(IntervalTreeNode *node,
|
||
|
|
uint64_t start, uint64_t last)
|
||
|
|
{
|
||
|
|
RBNode *rb = node->rb.rb_right, *prev;
|
||
|
|
|
||
|
|
while (true) {
|
||
|
|
/*
|
||
|
|
* Loop invariants:
|
||
|
|
* Cond1: node->start <= last
|
||
|
|
* rb == node->rb.rb_right
|
||
|
|
*
|
||
|
|
* First, search right subtree if suitable
|
||
|
|
*/
|
||
|
|
if (rb) {
|
||
|
|
IntervalTreeNode *right = rb_to_itree(rb);
|
||
|
|
|
||
|
|
if (start <= right->subtree_last) {
|
||
|
|
return interval_tree_subtree_search(right, start, last);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Move up the tree until we come from a node's left child */
|
||
|
|
do {
|
||
|
|
rb = rb_parent(&node->rb);
|
||
|
|
if (!rb) {
|
||
|
|
return NULL;
|
||
|
|
}
|
||
|
|
prev = &node->rb;
|
||
|
|
node = rb_to_itree(rb);
|
||
|
|
rb = node->rb.rb_right;
|
||
|
|
} while (prev == rb);
|
||
|
|
|
||
|
|
/* Check if the node intersects [start;last] */
|
||
|
|
if (last < node->start) { /* !Cond1 */
|
||
|
|
return NULL;
|
||
|
|
}
|
||
|
|
if (start <= node->last) { /* Cond2 */
|
||
|
|
return node;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Occasionally useful for calling from within the debugger. */
|
||
|
|
#if 0
|
||
|
|
static void debug_interval_tree_int(IntervalTreeNode *node,
|
||
|
|
const char *dir, int level)
|
||
|
|
{
|
||
|
|
printf("%4d %*s %s [%" PRIu64 ",%" PRIu64 "] subtree_last:%" PRIu64 "\n",
|
||
|
|
level, level + 1, dir, rb_is_red(&node->rb) ? "r" : "b",
|
||
|
|
node->start, node->last, node->subtree_last);
|
||
|
|
|
||
|
|
if (node->rb.rb_left) {
|
||
|
|
debug_interval_tree_int(rb_to_itree(node->rb.rb_left), "<", level + 1);
|
||
|
|
}
|
||
|
|
if (node->rb.rb_right) {
|
||
|
|
debug_interval_tree_int(rb_to_itree(node->rb.rb_right), ">", level + 1);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void debug_interval_tree(IntervalTreeNode *node);
|
||
|
|
void debug_interval_tree(IntervalTreeNode *node)
|
||
|
|
{
|
||
|
|
if (node) {
|
||
|
|
debug_interval_tree_int(node, "*", 0);
|
||
|
|
} else {
|
||
|
|
printf("null\n");
|
||
|
|
}
|
||
|
|
}
|
||
|
|
#endif
|