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// SPDX-License-Identifier: GPL-2.0-or-later | |
/* | |
Red Black Trees | |
(C) 1999 Andrea Arcangeli <andrea@suse.de> | |
(C) 2002 David Woodhouse <dwmw2@infradead.org> | |
(C) 2012 Michel Lespinasse <walken@google.com> | |
linux/lib/rbtree.c | |
*/ | |
#include <linux/rbtree_augmented.h> | |
#include <linux/export.h> | |
/* | |
* red-black trees properties: https://en.wikipedia.org/wiki/Rbtree | |
* | |
* 1) A node is either red or black | |
* 2) The root is black | |
* 3) All leaves (NULL) are black | |
* 4) Both children of every red node are black | |
* 5) Every simple path from root to leaves contains the same number | |
* of black nodes. | |
* | |
* 4 and 5 give the O(log n) guarantee, since 4 implies you cannot have two | |
* consecutive red nodes in a path and every red node is therefore followed by | |
* a black. So if B is the number of black nodes on every simple path (as per | |
* 5), then the longest possible path due to 4 is 2B. | |
* | |
* We shall indicate color with case, where black nodes are uppercase and red | |
* nodes will be lowercase. Unknown color nodes shall be drawn as red within | |
* parentheses and have some accompanying text comment. | |
*/ | |
/* | |
* Notes on lockless lookups: | |
* | |
* All stores to the tree structure (rb_left and rb_right) must be done using | |
* WRITE_ONCE(). And we must not inadvertently cause (temporary) loops in the | |
* tree structure as seen in program order. | |
* | |
* These two requirements will allow lockless iteration of the tree -- not | |
* correct iteration mind you, tree rotations are not atomic so a lookup might | |
* miss entire subtrees. | |
* | |
* But they do guarantee that any such traversal will only see valid elements | |
* and that it will indeed complete -- does not get stuck in a loop. | |
* | |
* It also guarantees that if the lookup returns an element it is the 'correct' | |
* one. But not returning an element does _NOT_ mean it's not present. | |
* | |
* NOTE: | |
* | |
* Stores to __rb_parent_color are not important for simple lookups so those | |
* are left undone as of now. Nor did I check for loops involving parent | |
* pointers. | |
*/ | |
static inline void rb_set_black(struct rb_node *rb) | |
{ | |
rb->__rb_parent_color |= RB_BLACK; | |
} | |
static inline struct rb_node *rb_red_parent(struct rb_node *red) | |
{ | |
return (struct rb_node *)red->__rb_parent_color; | |
} | |
/* | |
* Helper function for rotations: | |
* - old's parent and color get assigned to new | |
* - old gets assigned new as a parent and 'color' as a color. | |
*/ | |
static inline void | |
__rb_rotate_set_parents(struct rb_node *old, struct rb_node *new, | |
struct rb_root *root, int color) | |
{ | |
struct rb_node *parent = rb_parent(old); | |
new->__rb_parent_color = old->__rb_parent_color; | |
rb_set_parent_color(old, new, color); | |
__rb_change_child(old, new, parent, root); | |
} | |
static __always_inline void | |
__rb_insert(struct rb_node *node, struct rb_root *root, | |
void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
{ | |
struct rb_node *parent = rb_red_parent(node), *gparent, *tmp; | |
while (true) { | |
/* | |
* Loop invariant: node is red. | |
*/ | |
if (unlikely(!parent)) { | |
/* | |
* The inserted node is root. Either this is the | |
* first node, or we recursed at Case 1 below and | |
* are no longer violating 4). | |
*/ | |
rb_set_parent_color(node, NULL, RB_BLACK); | |
break; | |
} | |
/* | |
* If there is a black parent, we are done. | |
* Otherwise, take some corrective action as, | |
* per 4), we don't want a red root or two | |
* consecutive red nodes. | |
*/ | |
if(rb_is_black(parent)) | |
break; | |
gparent = rb_red_parent(parent); | |
tmp = gparent->rb_right; | |
if (parent != tmp) { /* parent == gparent->rb_left */ | |
if (tmp && rb_is_red(tmp)) { | |
/* | |
* Case 1 - node's uncle is red (color flips). | |
* | |
* G g | |
* / \ / \ | |
* p u --> P U | |
* / / | |
* n n | |
* | |
* However, since g's parent might be red, and | |
* 4) does not allow this, we need to recurse | |
* at g. | |
*/ | |
rb_set_parent_color(tmp, gparent, RB_BLACK); | |
rb_set_parent_color(parent, gparent, RB_BLACK); | |
node = gparent; | |
parent = rb_parent(node); | |
rb_set_parent_color(node, parent, RB_RED); | |
continue; | |
} | |
tmp = parent->rb_right; | |
if (node == tmp) { | |
/* | |
* Case 2 - node's uncle is black and node is | |
* the parent's right child (left rotate at parent). | |
* | |
* G G | |
* / \ / \ | |
* p U --> n U | |
* \ / | |
* n p | |
* | |
* This still leaves us in violation of 4), the | |
* continuation into Case 3 will fix that. | |
*/ | |
tmp = node->rb_left; | |
WRITE_ONCE(parent->rb_right, tmp); | |
WRITE_ONCE(node->rb_left, parent); | |
if (tmp) | |
rb_set_parent_color(tmp, parent, | |
RB_BLACK); | |
rb_set_parent_color(parent, node, RB_RED); | |
augment_rotate(parent, node); | |
parent = node; | |
tmp = node->rb_right; | |
} | |
/* | |
* Case 3 - node's uncle is black and node is | |
* the parent's left child (right rotate at gparent). | |
* | |
* G P | |
* / \ / \ | |
* p U --> n g | |
* / \ | |
* n U | |
*/ | |
WRITE_ONCE(gparent->rb_left, tmp); /* == parent->rb_right */ | |
WRITE_ONCE(parent->rb_right, gparent); | |
if (tmp) | |
rb_set_parent_color(tmp, gparent, RB_BLACK); | |
__rb_rotate_set_parents(gparent, parent, root, RB_RED); | |
augment_rotate(gparent, parent); | |
break; | |
} else { | |
tmp = gparent->rb_left; | |
if (tmp && rb_is_red(tmp)) { | |
/* Case 1 - color flips */ | |
rb_set_parent_color(tmp, gparent, RB_BLACK); | |
rb_set_parent_color(parent, gparent, RB_BLACK); | |
node = gparent; | |
parent = rb_parent(node); | |
rb_set_parent_color(node, parent, RB_RED); | |
continue; | |
} | |
tmp = parent->rb_left; | |
if (node == tmp) { | |
/* Case 2 - right rotate at parent */ | |
tmp = node->rb_right; | |
WRITE_ONCE(parent->rb_left, tmp); | |
WRITE_ONCE(node->rb_right, parent); | |
if (tmp) | |
rb_set_parent_color(tmp, parent, | |
RB_BLACK); | |
rb_set_parent_color(parent, node, RB_RED); | |
augment_rotate(parent, node); | |
parent = node; | |
tmp = node->rb_left; | |
} | |
/* Case 3 - left rotate at gparent */ | |
WRITE_ONCE(gparent->rb_right, tmp); /* == parent->rb_left */ | |
WRITE_ONCE(parent->rb_left, gparent); | |
if (tmp) | |
rb_set_parent_color(tmp, gparent, RB_BLACK); | |
__rb_rotate_set_parents(gparent, parent, root, RB_RED); | |
augment_rotate(gparent, parent); | |
break; | |
} | |
} | |
} | |
/* | |
* Inline version for rb_erase() use - we want to be able to inline | |
* and eliminate the dummy_rotate callback there | |
*/ | |
static __always_inline void | |
____rb_erase_color(struct rb_node *parent, struct rb_root *root, | |
void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
{ | |
struct rb_node *node = NULL, *sibling, *tmp1, *tmp2; | |
while (true) { | |
/* | |
* Loop invariants: | |
* - node is black (or NULL on first iteration) | |
* - node is not the root (parent is not NULL) | |
* - All leaf paths going through parent and node have a | |
* black node count that is 1 lower than other leaf paths. | |
*/ | |
sibling = parent->rb_right; | |
if (node != sibling) { /* node == parent->rb_left */ | |
if (rb_is_red(sibling)) { | |
/* | |
* Case 1 - left rotate at parent | |
* | |
* P S | |
* / \ / \ | |
* N s --> p Sr | |
* / \ / \ | |
* Sl Sr N Sl | |
*/ | |
tmp1 = sibling->rb_left; | |
WRITE_ONCE(parent->rb_right, tmp1); | |
WRITE_ONCE(sibling->rb_left, 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_right; | |
if (!tmp1 || rb_is_black(tmp1)) { | |
tmp2 = sibling->rb_left; | |
if (!tmp2 || rb_is_black(tmp2)) { | |
/* | |
* Case 2 - sibling color flip | |
* (p could be either color here) | |
* | |
* (p) (p) | |
* / \ / \ | |
* N S --> N s | |
* / \ / \ | |
* Sl Sr Sl Sr | |
* | |
* This leaves us violating 5) which | |
* can be fixed by flipping p to black | |
* 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 both | |
* 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; | |
WRITE_ONCE(sibling->rb_left, tmp1); | |
WRITE_ONCE(tmp2->rb_right, sibling); | |
WRITE_ONCE(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; | |
WRITE_ONCE(parent->rb_right, tmp2); | |
WRITE_ONCE(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; | |
WRITE_ONCE(parent->rb_left, tmp1); | |
WRITE_ONCE(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; | |
WRITE_ONCE(sibling->rb_right, tmp1); | |
WRITE_ONCE(tmp2->rb_left, sibling); | |
WRITE_ONCE(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; | |
WRITE_ONCE(parent->rb_left, tmp2); | |
WRITE_ONCE(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; | |
} | |
} | |
} | |
/* Non-inline version for rb_erase_augmented() use */ | |
void __rb_erase_color(struct rb_node *parent, struct rb_root *root, | |
void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
{ | |
____rb_erase_color(parent, root, augment_rotate); | |
} | |
EXPORT_SYMBOL(__rb_erase_color); | |
/* | |
* Non-augmented rbtree manipulation functions. | |
* | |
* We use dummy augmented callbacks here, and have the compiler optimize them | |
* out of the rb_insert_color() and rb_erase() function definitions. | |
*/ | |
static inline void dummy_propagate(struct rb_node *node, struct rb_node *stop) {} | |
static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {} | |
static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {} | |
static const struct rb_augment_callbacks dummy_callbacks = { | |
.propagate = dummy_propagate, | |
.copy = dummy_copy, | |
.rotate = dummy_rotate | |
}; | |
void rb_insert_color(struct rb_node *node, struct rb_root *root) | |
{ | |
__rb_insert(node, root, dummy_rotate); | |
} | |
EXPORT_SYMBOL(rb_insert_color); | |
void rb_erase(struct rb_node *node, struct rb_root *root) | |
{ | |
struct rb_node *rebalance; | |
rebalance = __rb_erase_augmented(node, root, &dummy_callbacks); | |
if (rebalance) | |
____rb_erase_color(rebalance, root, dummy_rotate); | |
} | |
EXPORT_SYMBOL(rb_erase); | |
/* | |
* Augmented rbtree manipulation functions. | |
* | |
* This instantiates the same __always_inline functions as in the non-augmented | |
* case, but this time with user-defined callbacks. | |
*/ | |
void __rb_insert_augmented(struct rb_node *node, struct rb_root *root, | |
void (*augment_rotate)(struct rb_node *old, struct rb_node *new)) | |
{ | |
__rb_insert(node, root, augment_rotate); | |
} | |
EXPORT_SYMBOL(__rb_insert_augmented); | |
/* | |
* This function returns the first node (in sort order) of the tree. | |
*/ | |
struct rb_node *rb_first(const struct rb_root *root) | |
{ | |
struct rb_node *n; | |
n = root->rb_node; | |
if (!n) | |
return NULL; | |
while (n->rb_left) | |
n = n->rb_left; | |
return n; | |
} | |
EXPORT_SYMBOL(rb_first); | |
struct rb_node *rb_last(const struct rb_root *root) | |
{ | |
struct rb_node *n; | |
n = root->rb_node; | |
if (!n) | |
return NULL; | |
while (n->rb_right) | |
n = n->rb_right; | |
return n; | |
} | |
EXPORT_SYMBOL(rb_last); | |
struct rb_node *rb_next(const struct rb_node *node) | |
{ | |
struct rb_node *parent; | |
if (RB_EMPTY_NODE(node)) | |
return NULL; | |
/* | |
* If we have a right-hand child, go down and then left as far | |
* as we can. | |
*/ | |
if (node->rb_right) { | |
node = node->rb_right; | |
while (node->rb_left) | |
node = node->rb_left; | |
return (struct rb_node *)node; | |
} | |
/* | |
* No right-hand children. Everything down and left is smaller than us, | |
* so any 'next' node must be in the general direction of our parent. | |
* Go up the tree; any time the ancestor is a right-hand child of its | |
* parent, keep going up. First time it's a left-hand child of its | |
* parent, said parent is our 'next' node. | |
*/ | |
while ((parent = rb_parent(node)) && node == parent->rb_right) | |
node = parent; | |
return parent; | |
} | |
EXPORT_SYMBOL(rb_next); | |
struct rb_node *rb_prev(const struct rb_node *node) | |
{ | |
struct rb_node *parent; | |
if (RB_EMPTY_NODE(node)) | |
return NULL; | |
/* | |
* If we have a left-hand child, go down and then right as far | |
* as we can. | |
*/ | |
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; | |
} | |
EXPORT_SYMBOL(rb_prev); | |
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); | |
} | |
EXPORT_SYMBOL(rb_replace_node); | |
void rb_replace_node_rcu(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); | |
/* Set the parent's pointer to the new node last after an RCU barrier | |
* so that the pointers onwards are seen to be set correctly when doing | |
* an RCU walk over the tree. | |
*/ | |
__rb_change_child_rcu(victim, new, parent, root); | |
} | |
EXPORT_SYMBOL(rb_replace_node_rcu); | |
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; | |
} | |
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); |