forked from Minki/linux
9d9e6f9703
convert arch/x86/mm/pat_rbtree.c to the proposed augmented rbtree api and remove the old augmented rbtree implementation. 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>
647 lines
17 KiB
C
647 lines
17 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) {}
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static inline void dummy_copy(struct rb_node *old, struct rb_node *new) {}
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static inline void dummy_rotate(struct rb_node *old, struct rb_node *new) {}
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static const struct rb_augment_callbacks dummy_callbacks = {
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dummy_propagate, dummy_copy, dummy_rotate
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};
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void rb_insert_color(struct rb_node *node, struct rb_root *root)
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{
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__rb_insert(node, root, dummy_rotate);
|
|
}
|
|
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);
|
|
|
|
/*
|
|
* 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);
|