14b94af0b2
Introduce new augmented rbtree APIs that allow minimal recalculation of augmented node information. A new callback is added to the rbtree insertion and erase rebalancing functions, to be called on each tree rotations. Such rotations preserve the subtree's root augmented value, but require recalculation of the one child that was previously located at the subtree root. In the insertion case, the handcoded search phase must be updated to maintain the augmented information on insertion, and then the rbtree coloring/rebalancing algorithms keep it up to date. In the erase case, things are more complicated since it is library code that manipulates the rbtree in order to remove internal nodes. This requires a couple additional callbacks to copy a subtree's augmented value when a new root is stitched in, and to recompute augmented values down the ancestry path when a node is removed from the tree. In order to preserve maximum speed for the non-augmented case, we provide two versions of each tree manipulation function. rb_insert_augmented() is the augmented equivalent of rb_insert_color(), and rb_erase_augmented() is the augmented equivalent of rb_erase(). Signed-off-by: Michel Lespinasse <walken@google.com> Acked-by: Rik 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: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
717 lines
19 KiB
C
717 lines
19 KiB
C
/*
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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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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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linux/lib/rbtree.c
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*/
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#include <linux/rbtree.h>
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#include <linux/export.h>
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/*
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* red-black trees properties: http://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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#define RB_RED 0
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#define RB_BLACK 1
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#define __rb_parent(pc) ((struct rb_node *)(pc & ~3))
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#define __rb_color(pc) ((pc) & 1)
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#define __rb_is_black(pc) __rb_color(pc)
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#define __rb_is_red(pc) (!__rb_color(pc))
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#define rb_color(rb) __rb_color((rb)->__rb_parent_color)
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#define rb_is_red(rb) __rb_is_red((rb)->__rb_parent_color)
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#define rb_is_black(rb) __rb_is_black((rb)->__rb_parent_color)
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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 void rb_set_parent(struct rb_node *rb, struct rb_node *p)
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{
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rb->__rb_parent_color = rb_color(rb) | (unsigned long)p;
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}
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static inline void rb_set_parent_color(struct rb_node *rb,
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struct rb_node *p, int color)
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{
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rb->__rb_parent_color = (unsigned long)p | color;
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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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static inline void
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__rb_change_child(struct rb_node *old, struct rb_node *new,
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struct rb_node *parent, struct rb_root *root)
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{
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if (parent) {
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if (parent->rb_left == old)
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parent->rb_left = new;
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else
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parent->rb_right = new;
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} else
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root->rb_node = new;
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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 there is a black parent, we are done.
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* Otherwise, take some corrective action as we don't
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* want a red root or two consecutive red nodes.
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*/
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if (!parent) {
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rb_set_parent_color(node, NULL, RB_BLACK);
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break;
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} else 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 - 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 - 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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parent->rb_right = tmp = node->rb_left;
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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 - 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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gparent->rb_left = tmp; /* == parent->rb_right */
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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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parent->rb_left = tmp = node->rb_right;
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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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gparent->rb_right = tmp; /* == parent->rb_left */
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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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static __always_inline void
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__rb_erase_color(struct rb_node *parent, struct rb_root *root,
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const struct rb_augment_callbacks *augment)
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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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parent->rb_right = tmp1 = sibling->rb_left;
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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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sibling->rb_left = tmp1 = tmp2->rb_right;
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tmp2->rb_right = sibling;
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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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parent->rb_right = tmp2 = sibling->rb_left;
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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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parent->rb_left = tmp1 = sibling->rb_right;
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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 - right rotate at sibling */
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sibling->rb_right = tmp1 = tmp2->rb_left;
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tmp2->rb_left = sibling;
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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 - left rotate at parent + color flips */
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parent->rb_left = tmp2 = sibling->rb_right;
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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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static __always_inline void
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__rb_erase(struct rb_node *node, struct rb_root *root,
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const struct rb_augment_callbacks *augment)
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{
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struct rb_node *child = node->rb_right, *tmp = node->rb_left;
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struct rb_node *parent, *rebalance;
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unsigned long pc;
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if (!tmp) {
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/*
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* Case 1: node to erase has no more than 1 child (easy!)
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*
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* Note that if there is one child it must be red due to 5)
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* and node must be black due to 4). We adjust colors locally
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* so as to bypass __rb_erase_color() later on.
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*/
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pc = node->__rb_parent_color;
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parent = __rb_parent(pc);
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__rb_change_child(node, child, parent, root);
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if (child) {
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child->__rb_parent_color = pc;
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rebalance = NULL;
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} else
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rebalance = __rb_is_black(pc) ? parent : NULL;
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tmp = parent;
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} else if (!child) {
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/* Still case 1, but this time the child is node->rb_left */
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tmp->__rb_parent_color = pc = node->__rb_parent_color;
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parent = __rb_parent(pc);
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__rb_change_child(node, tmp, parent, root);
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rebalance = NULL;
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tmp = parent;
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} else {
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struct rb_node *successor = child, *child2;
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tmp = child->rb_left;
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if (!tmp) {
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/*
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* Case 2: node's successor is its right child
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*
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* (n) (s)
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* / \ / \
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* (x) (s) -> (x) (c)
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* \
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* (c)
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*/
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parent = successor;
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child2 = successor->rb_right;
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augment->copy(node, successor);
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} else {
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/*
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* Case 3: node's successor is leftmost under
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* node's right child subtree
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*
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* (n) (s)
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* / \ / \
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* (x) (y) -> (x) (y)
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* / /
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* (p) (p)
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* / /
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* (s) (c)
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* \
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* (c)
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*/
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do {
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parent = successor;
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successor = tmp;
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tmp = tmp->rb_left;
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} while (tmp);
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parent->rb_left = child2 = successor->rb_right;
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successor->rb_right = child;
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rb_set_parent(child, successor);
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augment->copy(node, successor);
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augment->propagate(parent, successor);
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}
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successor->rb_left = tmp = node->rb_left;
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rb_set_parent(tmp, successor);
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pc = node->__rb_parent_color;
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tmp = __rb_parent(pc);
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__rb_change_child(node, successor, tmp, root);
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if (child2) {
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successor->__rb_parent_color = pc;
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rb_set_parent_color(child2, parent, RB_BLACK);
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rebalance = NULL;
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} else {
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unsigned long pc2 = successor->__rb_parent_color;
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successor->__rb_parent_color = pc;
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rebalance = __rb_is_black(pc2) ? parent : NULL;
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}
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tmp = successor;
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}
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augment->propagate(tmp, NULL);
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if (rebalance)
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__rb_erase_color(rebalance, root, augment);
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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) {}
|
|
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 = {
|
|
dummy_propagate, dummy_copy, 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)
|
|
{
|
|
__rb_erase(node, root, &dummy_callbacks);
|
|
}
|
|
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);
|
|
|
|
void rb_erase_augmented(struct rb_node *node, struct rb_root *root,
|
|
const struct rb_augment_callbacks *augment)
|
|
{
|
|
__rb_erase(node, root, augment);
|
|
}
|
|
EXPORT_SYMBOL(rb_erase_augmented);
|
|
|
|
static void rb_augment_path(struct rb_node *node, rb_augment_f func, void *data)
|
|
{
|
|
struct rb_node *parent;
|
|
|
|
up:
|
|
func(node, data);
|
|
parent = rb_parent(node);
|
|
if (!parent)
|
|
return;
|
|
|
|
if (node == parent->rb_left && parent->rb_right)
|
|
func(parent->rb_right, data);
|
|
else if (parent->rb_left)
|
|
func(parent->rb_left, data);
|
|
|
|
node = parent;
|
|
goto up;
|
|
}
|
|
|
|
/*
|
|
* after inserting @node into the tree, update the tree to account for
|
|
* both the new entry and any damage done by rebalance
|
|
*/
|
|
void rb_augment_insert(struct rb_node *node, rb_augment_f func, void *data)
|
|
{
|
|
if (node->rb_left)
|
|
node = node->rb_left;
|
|
else if (node->rb_right)
|
|
node = node->rb_right;
|
|
|
|
rb_augment_path(node, func, data);
|
|
}
|
|
EXPORT_SYMBOL(rb_augment_insert);
|
|
|
|
/*
|
|
* before removing the node, find the deepest node on the rebalance path
|
|
* that will still be there after @node gets removed
|
|
*/
|
|
struct rb_node *rb_augment_erase_begin(struct rb_node *node)
|
|
{
|
|
struct rb_node *deepest;
|
|
|
|
if (!node->rb_right && !node->rb_left)
|
|
deepest = rb_parent(node);
|
|
else if (!node->rb_right)
|
|
deepest = node->rb_left;
|
|
else if (!node->rb_left)
|
|
deepest = node->rb_right;
|
|
else {
|
|
deepest = rb_next(node);
|
|
if (deepest->rb_right)
|
|
deepest = deepest->rb_right;
|
|
else if (rb_parent(deepest) != node)
|
|
deepest = rb_parent(deepest);
|
|
}
|
|
|
|
return deepest;
|
|
}
|
|
EXPORT_SYMBOL(rb_augment_erase_begin);
|
|
|
|
/*
|
|
* after removal, update the tree to account for the removed entry
|
|
* and any rebalance damage.
|
|
*/
|
|
void rb_augment_erase_end(struct rb_node *node, rb_augment_f func, void *data)
|
|
{
|
|
if (node)
|
|
rb_augment_path(node, func, data);
|
|
}
|
|
EXPORT_SYMBOL(rb_augment_erase_end);
|
|
|
|
/*
|
|
* 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);
|
|
|
|
/* Set the surrounding nodes to point to the replacement */
|
|
__rb_change_child(victim, new, parent, root);
|
|
if (victim->rb_left)
|
|
rb_set_parent(victim->rb_left, new);
|
|
if (victim->rb_right)
|
|
rb_set_parent(victim->rb_right, new);
|
|
|
|
/* Copy the pointers/colour from the victim to the replacement */
|
|
*new = *victim;
|
|
}
|
|
EXPORT_SYMBOL(rb_replace_node);
|