Commit 46b6135a authored by Michel Lespinasse's avatar Michel Lespinasse Committed by Linus Torvalds

rbtree: handle 1-child recoloring in rb_erase() instead of rb_erase_color()

An interesting observation for rb_erase() is that when a node has
exactly one child, the node must be black and the child must be red.
An interesting consequence is that removing such a node can be done by
simply replacing it with its child and making the child black,
which we can do efficiently in rb_erase(). __rb_erase_color() then
only needs to handle the no-childs case and can be modified accordingly.
Signed-off-by: default avatarMichel Lespinasse <walken@google.com>
Acked-by: default avatarRik van Riel <riel@redhat.com>
Cc: Peter Zijlstra <a.p.zijlstra@chello.nl>
Cc: Andrea Arcangeli <aarcange@redhat.com>
Cc: David Woodhouse <dwmw2@infradead.org>
Signed-off-by: default avatarAndrew Morton <akpm@linux-foundation.org>
Signed-off-by: default avatarLinus Torvalds <torvalds@linux-foundation.org>
parent 60670b80
...@@ -2,6 +2,7 @@ ...@@ -2,6 +2,7 @@
Red Black Trees Red Black Trees
(C) 1999 Andrea Arcangeli <andrea@suse.de> (C) 1999 Andrea Arcangeli <andrea@suse.de>
(C) 2002 David Woodhouse <dwmw2@infradead.org> (C) 2002 David Woodhouse <dwmw2@infradead.org>
(C) 2012 Michel Lespinasse <walken@google.com>
This program is free software; you can redistribute it and/or modify This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by it under the terms of the GNU General Public License as published by
...@@ -50,6 +51,11 @@ ...@@ -50,6 +51,11 @@
#define rb_is_red(r) (!rb_color(r)) #define rb_is_red(r) (!rb_color(r))
#define rb_is_black(r) rb_color(r) #define rb_is_black(r) rb_color(r)
static inline void rb_set_black(struct rb_node *rb)
{
rb->__rb_parent_color |= RB_BLACK;
}
static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p) static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
{ {
rb->__rb_parent_color = rb_color(rb) | (unsigned long)p; rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
...@@ -214,27 +220,18 @@ void rb_insert_color(struct rb_node *node, struct rb_root *root) ...@@ -214,27 +220,18 @@ void rb_insert_color(struct rb_node *node, struct rb_root *root)
} }
EXPORT_SYMBOL(rb_insert_color); EXPORT_SYMBOL(rb_insert_color);
static void __rb_erase_color(struct rb_node *node, struct rb_node *parent, static void __rb_erase_color(struct rb_node *parent, struct rb_root *root)
struct rb_root *root)
{ {
struct rb_node *sibling, *tmp1, *tmp2; struct rb_node *node = NULL, *sibling, *tmp1, *tmp2;
while (true) { while (true) {
/* /*
* Loop invariant: all leaf paths going through node have a * 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. * black node count that is 1 lower than other leaf paths.
*
* If node is red, we can flip it to black to adjust.
* If node is the root, all leaf paths go through it.
* Otherwise, we need to adjust the tree through color flips
* and tree rotations as per one of the 4 cases below.
*/ */
if (node && rb_is_red(node)) {
rb_set_parent_color(node, parent, RB_BLACK);
break;
} else if (!parent) {
break;
}
sibling = parent->rb_right; sibling = parent->rb_right;
if (node != sibling) { /* node == parent->rb_left */ if (node != sibling) { /* node == parent->rb_left */
if (rb_is_red(sibling)) { if (rb_is_red(sibling)) {
...@@ -268,18 +265,23 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent, ...@@ -268,18 +265,23 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
* / \ / \ * / \ / \
* Sl Sr Sl Sr * Sl Sr Sl Sr
* *
* This leaves us violating 5), so * This leaves us violating 5) which
* recurse at p. If p is red, the * can be fixed by flipping p to black
* recursion will just flip it to black * if it was red, or by recursing at p.
* and exit. If coming from Case 1, * p is red when coming from Case 1.
* p is known to be red.
*/ */
rb_set_parent_color(sibling, parent, rb_set_parent_color(sibling, parent,
RB_RED); RB_RED);
if (rb_is_red(parent))
rb_set_black(parent);
else {
node = parent; node = parent;
parent = rb_parent(node); parent = rb_parent(node);
if (parent)
continue; continue;
} }
break;
}
/* /*
* Case 3 - right rotate at sibling * Case 3 - right rotate at sibling
* (p could be either color here) * (p could be either color here)
...@@ -339,10 +341,16 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent, ...@@ -339,10 +341,16 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
/* Case 2 - sibling color flip */ /* Case 2 - sibling color flip */
rb_set_parent_color(sibling, parent, rb_set_parent_color(sibling, parent,
RB_RED); RB_RED);
if (rb_is_red(parent))
rb_set_black(parent);
else {
node = parent; node = parent;
parent = rb_parent(node); parent = rb_parent(node);
if (parent)
continue; continue;
} }
break;
}
/* Case 3 - right rotate at sibling */ /* Case 3 - right rotate at sibling */
sibling->rb_right = tmp1 = tmp2->rb_left; sibling->rb_right = tmp1 = tmp2->rb_left;
tmp2->rb_left = sibling; tmp2->rb_left = sibling;
...@@ -369,23 +377,31 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent, ...@@ -369,23 +377,31 @@ static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
void rb_erase(struct rb_node *node, struct rb_root *root) void rb_erase(struct rb_node *node, struct rb_root *root)
{ {
struct rb_node *child = node->rb_right, *tmp = node->rb_left; struct rb_node *child = node->rb_right, *tmp = node->rb_left;
struct rb_node *parent; struct rb_node *parent, *rebalance;
int color;
if (!tmp) { if (!tmp) {
case1: /*
/* Case 1: node to erase has no more than 1 child (easy!) */ * 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.
*/
parent = rb_parent(node); parent = rb_parent(node);
color = rb_color(node);
if (child)
rb_set_parent(child, parent);
__rb_change_child(node, child, parent, root); __rb_change_child(node, child, parent, root);
if (child) {
rb_set_parent_color(child, parent, RB_BLACK);
rebalance = NULL;
} else {
rebalance = rb_is_black(node) ? parent : NULL;
}
} else if (!child) { } else if (!child) {
/* Still case 1, but this time the child is node->rb_left */ /* Still case 1, but this time the child is node->rb_left */
child = tmp; parent = rb_parent(node);
goto case1; __rb_change_child(node, tmp, parent, root);
rb_set_parent_color(tmp, parent, RB_BLACK);
rebalance = NULL;
} else { } else {
struct rb_node *old = node, *left; struct rb_node *old = node, *left;
...@@ -397,26 +413,29 @@ void rb_erase(struct rb_node *node, struct rb_root *root) ...@@ -397,26 +413,29 @@ void rb_erase(struct rb_node *node, struct rb_root *root)
child = node->rb_right; child = node->rb_right;
parent = rb_parent(node); parent = rb_parent(node);
color = rb_color(node);
if (parent == old) { if (parent == old) {
parent = node; parent = node;
} else { } else {
if (child)
rb_set_parent(child, parent);
parent->rb_left = child; parent->rb_left = child;
node->rb_right = old->rb_right; node->rb_right = old->rb_right;
rb_set_parent(old->rb_right, node); rb_set_parent(old->rb_right, node);
} }
if (child) {
rb_set_parent_color(child, parent, RB_BLACK);
rebalance = NULL;
} else {
rebalance = rb_is_black(node) ? parent : NULL;
}
node->__rb_parent_color = old->__rb_parent_color; node->__rb_parent_color = old->__rb_parent_color;
node->rb_left = old->rb_left; node->rb_left = old->rb_left;
rb_set_parent(old->rb_left, node); rb_set_parent(old->rb_left, node);
} }
if (color == RB_BLACK) if (rebalance)
__rb_erase_color(child, parent, root); __rb_erase_color(rebalance, root);
} }
EXPORT_SYMBOL(rb_erase); EXPORT_SYMBOL(rb_erase);
......
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