/*-
* Copyright (c) 2001 The NetBSD Foundation, Inc.
* All rights reserved.
*
* This code is derived from software contributed to The NetBSD Foundation
* by Matt Thomas <matt@3am-software.com>.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS
* ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
* TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
* Based on: NetBSD: rb.c,v 1.6 2010/04/30 13:58:09 joerg Exp
*/
#include "archive_platform.h"
#include <stddef.h>
#include "archive_rb.h"
/* Keep in sync with archive_rb.h */
#define RB_DIR_LEFT 0
#define RB_DIR_RIGHT 1
#define RB_DIR_OTHER 1
#define rb_left rb_nodes[RB_DIR_LEFT]
#define rb_right rb_nodes[RB_DIR_RIGHT]
#define RB_FLAG_POSITION 0x2
#define RB_FLAG_RED 0x1
#define RB_FLAG_MASK (RB_FLAG_POSITION|RB_FLAG_RED)
#define RB_FATHER(rb) \
((struct archive_rb_node *)((rb)->rb_info & ~RB_FLAG_MASK))
#define RB_SET_FATHER(rb, father) \
((void)((rb)->rb_info = (uintptr_t)(father)|((rb)->rb_info & RB_FLAG_MASK)))
#define RB_SENTINEL_P(rb) ((rb) == NULL)
#define RB_LEFT_SENTINEL_P(rb) RB_SENTINEL_P((rb)->rb_left)
#define RB_RIGHT_SENTINEL_P(rb) RB_SENTINEL_P((rb)->rb_right)
#define RB_FATHER_SENTINEL_P(rb) RB_SENTINEL_P(RB_FATHER((rb)))
#define RB_CHILDLESS_P(rb) \
(RB_SENTINEL_P(rb) || (RB_LEFT_SENTINEL_P(rb) && RB_RIGHT_SENTINEL_P(rb)))
#define RB_TWOCHILDREN_P(rb) \
(!RB_SENTINEL_P(rb) && !RB_LEFT_SENTINEL_P(rb) && !RB_RIGHT_SENTINEL_P(rb))
#define RB_POSITION(rb) \
(((rb)->rb_info & RB_FLAG_POSITION) ? RB_DIR_RIGHT : RB_DIR_LEFT)
#define RB_RIGHT_P(rb) (RB_POSITION(rb) == RB_DIR_RIGHT)
#define RB_LEFT_P(rb) (RB_POSITION(rb) == RB_DIR_LEFT)
#define RB_RED_P(rb) (!RB_SENTINEL_P(rb) && ((rb)->rb_info & RB_FLAG_RED) != 0)
#define RB_BLACK_P(rb) (RB_SENTINEL_P(rb) || ((rb)->rb_info & RB_FLAG_RED) == 0)
#define RB_MARK_RED(rb) ((void)((rb)->rb_info |= RB_FLAG_RED))
#define RB_MARK_BLACK(rb) ((void)((rb)->rb_info &= ~RB_FLAG_RED))
#define RB_INVERT_COLOR(rb) ((void)((rb)->rb_info ^= RB_FLAG_RED))
#define RB_ROOT_P(rbt, rb) ((rbt)->rbt_root == (rb))
#define RB_SET_POSITION(rb, position) \
((void)((position) ? ((rb)->rb_info |= RB_FLAG_POSITION) : \
((rb)->rb_info &= ~RB_FLAG_POSITION)))
#define RB_ZERO_PROPERTIES(rb) ((void)((rb)->rb_info &= ~RB_FLAG_MASK))
#define RB_COPY_PROPERTIES(dst, src) \
((void)((dst)->rb_info ^= ((dst)->rb_info ^ (src)->rb_info) & RB_FLAG_MASK))
#define RB_SWAP_PROPERTIES(a, b) do { \
uintptr_t xorinfo = ((a)->rb_info ^ (b)->rb_info) & RB_FLAG_MASK; \
(a)->rb_info ^= xorinfo; \
(b)->rb_info ^= xorinfo; \
} while (/*CONSTCOND*/ 0)
static void __archive_rb_tree_insert_rebalance(struct archive_rb_tree *,
struct archive_rb_node *);
static void __archive_rb_tree_removal_rebalance(struct archive_rb_tree *,
struct archive_rb_node *, unsigned int);
#define RB_SENTINEL_NODE NULL
#define T 1
#define F 0
void
__archive_rb_tree_init(struct archive_rb_tree *rbt,
const struct archive_rb_tree_ops *ops)
{
rbt->rbt_ops = ops;
*((struct archive_rb_node **)&rbt->rbt_root) = RB_SENTINEL_NODE;
}
struct archive_rb_node *
__archive_rb_tree_find_node(struct archive_rb_tree *rbt, const void *key)
{
archive_rbto_compare_key_fn compare_key = rbt->rbt_ops->rbto_compare_key;
struct archive_rb_node *parent = rbt->rbt_root;
while (!RB_SENTINEL_P(parent)) {
const signed int diff = (*compare_key)(parent, key);
if (diff == 0)
return parent;
parent = parent->rb_nodes[diff > 0];
}
return NULL;
}
struct archive_rb_node *
__archive_rb_tree_find_node_geq(struct archive_rb_tree *rbt, const void *key)
{
archive_rbto_compare_key_fn compare_key = rbt->rbt_ops->rbto_compare_key;
struct archive_rb_node *parent = rbt->rbt_root;
struct archive_rb_node *last = NULL;
while (!RB_SENTINEL_P(parent)) {
const signed int diff = (*compare_key)(parent, key);
if (diff == 0)
return parent;
if (diff < 0)
last = parent;
parent = parent->rb_nodes[diff > 0];
}
return last;
}
struct archive_rb_node *
__archive_rb_tree_find_node_leq(struct archive_rb_tree *rbt, const void *key)
{
archive_rbto_compare_key_fn compare_key = rbt->rbt_ops->rbto_compare_key;
struct archive_rb_node *parent = rbt->rbt_root;
struct archive_rb_node *last = NULL;
while (!RB_SENTINEL_P(parent)) {
const signed int diff = (*compare_key)(parent, key);
if (diff == 0)
return parent;
if (diff > 0)
last = parent;
parent = parent->rb_nodes[diff > 0];
}
return last;
}
int
__archive_rb_tree_insert_node(struct archive_rb_tree *rbt,
struct archive_rb_node *self)
{
archive_rbto_compare_nodes_fn compare_nodes = rbt->rbt_ops->rbto_compare_nodes;
struct archive_rb_node *parent, *tmp;
unsigned int position;
int rebalance;
tmp = rbt->rbt_root;
/*
* This is a hack. Because rbt->rbt_root is just a
* struct archive_rb_node *, just like rb_node->rb_nodes[RB_DIR_LEFT],
* we can use this fact to avoid a lot of tests for root and know
* that even at root, updating
* RB_FATHER(rb_node)->rb_nodes[RB_POSITION(rb_node)] will
* update rbt->rbt_root.
*/
parent = (struct archive_rb_node *)(void *)&rbt->rbt_root;
position = RB_DIR_LEFT;
/*
* Find out where to place this new leaf.
*/
while (!RB_SENTINEL_P(tmp)) {
const signed int diff = (*compare_nodes)(tmp, self);
if (diff == 0) {
/*
* Node already exists; don't insert.
*/
return F;
}
parent = tmp;
position = (diff > 0);
tmp = parent->rb_nodes[position];
}
/*
* Initialize the node and insert as a leaf into the tree.
*/
RB_SET_FATHER(self, parent);
RB_SET_POSITION(self, position);
if (parent == (struct archive_rb_node *)(void *)&rbt->rbt_root) {
RB_MARK_BLACK(self); /* root is always black */
rebalance = F;
} else {
/*
* All new nodes are colored red. We only need to rebalance
* if our parent is also red.
*/
RB_MARK_RED(self);
rebalance = RB_RED_P(parent);
}
self->rb_left = parent->rb_nodes[position];
self->rb_right = parent->rb_nodes[position];
parent->rb_nodes[position] = self;
/*
* Rebalance tree after insertion
*/
if (rebalance)
__archive_rb_tree_insert_rebalance(rbt, self);
return T;
}
/*
* Swap the location and colors of 'self' and its child @ which. The child
* can not be a sentinel node. This is our rotation function. However,
* since it preserves coloring, it great simplifies both insertion and
* removal since rotation almost always involves the exchanging of colors
* as a separate step.
*/
/*ARGSUSED*/
static void
__archive_rb_tree_reparent_nodes(
struct archive_rb_node *old_father, const unsigned int which)
{
const unsigned int other = which ^ RB_DIR_OTHER;
struct archive_rb_node * const grandpa = RB_FATHER(old_father);
struct archive_rb_node * const old_child = old_father->rb_nodes[which];
struct archive_rb_node * const new_father = old_child;
struct archive_rb_node * const new_child = old_father;
if (new_father == NULL)
return;
/*
* Exchange descendant linkages.
*/
grandpa->rb_nodes[RB_POSITION(old_father)] = new_father;
new_child->rb_nodes[which] = old_child->rb_nodes[other];
new_father->rb_nodes[other] = new_child;
/*
* Update ancestor linkages
*/
RB_SET_FATHER(new_father, grandpa);
RB_SET_FATHER(new_child, new_father);
/*
* Exchange properties between new_father and new_child. The only
* change is that new_child's position is now on the other side.
*/
RB_SWAP_PROPERTIES(new_father, new_child);
RB_SET_POSITION(new_child, other);
/*
* Make sure to reparent the new child to ourself.
*/
if (!RB_SENTINEL_P(new_child->rb_nodes[which])) {
RB_SET_FATHER(new_child->rb_nodes[which], new_child);
RB_SET_POSITION(new_child->rb_nodes[which], which);
}
}
static void
__archive_rb_tree_insert_rebalance(struct archive_rb_tree *rbt,
struct archive_rb_node *self)
{
struct archive_rb_node * father = RB_FATHER(self);
struct archive_rb_node * grandpa;
struct archive_rb_node * uncle;
unsigned int which;
unsigned int other;
for (;;) {
/*
* We are red and our parent is red, therefore we must have a
* grandfather and he must be black.
*/
grandpa = RB_FATHER(father);
which = (father == grandpa->rb_right);
other = which ^ RB_DIR_OTHER;
uncle = grandpa->rb_nodes[other];
if (RB_BLACK_P(uncle))
break;
/*
* Case 1: our uncle is red
* Simply invert the colors of our parent and
* uncle and make our grandparent red. And
* then solve the problem up at his level.
*/
RB_MARK_BLACK(uncle);
RB_MARK_BLACK(father);
if (RB_ROOT_P(rbt, grandpa)) {
/*
* If our grandpa is root, don't bother
* setting him to red, just return.
*/
return;
}
RB_MARK_RED(grandpa);
self = grandpa;
father = RB_FATHER(self);
if (RB_BLACK_P(father)) {
/*
* If our great-grandpa is black, we're done.
*/
return;
}
}
/*
* Case 2&3: our uncle is black.
*/
if (self == father->rb_nodes[other]) {
/*
* Case 2: we are on the same side as our uncle
* Swap ourselves with our parent so this case
* becomes case 3. Basically our parent becomes our
* child.
*/
__archive_rb_tree_reparent_nodes(father, other);
}
/*
* Case 3: we are opposite a child of a black uncle.
* Swap our parent and grandparent. Since our grandfather
* is black, our father will become black and our new sibling
* (former grandparent) will become red.
*/
__archive_rb_tree_reparent_nodes(grandpa, which);
/*
* Final step: Set the root to black.
*/
RB_MARK_BLACK(rbt->rbt_root);
}
static void
__archive_rb_tree_prune_node(struct archive_rb_tree *rbt,
struct archive_rb_node *self, int rebalance)
{
const unsigned int which = RB_POSITION(self);
struct archive_rb_node *father = RB_FATHER(self);
/*
* Since we are childless, we know that self->rb_left is pointing
* to the sentinel node.
*/
father->rb_nodes[which] = self->rb_left;
/*
* Rebalance if requested.
*/
if (rebalance)
__archive_rb_tree_removal_rebalance(rbt, father, which);
}
/*
* When deleting an interior node
*/
static void
__archive_rb_tree_swap_prune_and_rebalance(struct archive_rb_tree *rbt,
struct archive_rb_node *self, struct archive_rb_node *standin)
{
const unsigned int standin_which = RB_POSITION(standin);
unsigned int standin_other = standin_which ^ RB_DIR_OTHER;
struct archive_rb_node *standin_son;
struct archive_rb_node *standin_father = RB_FATHER(standin);
int rebalance = RB_BLACK_P(standin);
if (standin_father == self) {
/*
* As a child of self, any children would be opposite of
* our parent.
*/
standin_son = standin->rb_nodes[standin_which];
} else {
/*
* Since we aren't a child of self, any children would be
* on the same side as our parent.
*/
standin_son = standin->rb_nodes[standin_other];
}
if (RB_RED_P(standin_son)) {
/*
* We know we have a red child so if we flip it to black
* we don't have to rebalance.
*/
RB_MARK_BLACK(standin_son);
rebalance = F;
if (standin_father != self) {
/*
* Change the son's parentage to point to his grandpa.
*/
RB_SET_FATHER(standin_son, standin_father);
RB_SET_POSITION(standin_son, standin_which);
}
}
if (standin_father == self) {
/*
* If we are about to delete the standin's father, then when
* we call rebalance, we need to use ourselves as our father.
* Otherwise remember our original father. Also, since we are
* our standin's father we only need to reparent the standin's
* brother.
*
* | R --> S |
* | Q S --> Q T |
* | t --> |
*
* Have our son/standin adopt his brother as his new son.
*/
standin_father = standin;
} else {
/*
* | R --> S . |
* | / \ | T --> / \ | / |
* | ..... | S --> ..... | T |
*
* Sever standin's connection to his father.
*/
standin_father->rb_nodes[standin_which] = standin_son;
/*
* Adopt the far son.
*/
standin->rb_nodes[standin_other] = self->rb_nodes[standin_other];
RB_SET_FATHER(standin->rb_nodes[standin_other], standin);
/*
* Use standin_other because we need to preserve standin_which
* for the removal_rebalance.
*/
standin_other = standin_which;
}
/*
* Move the only remaining son to our standin. If our standin is our
* son, this will be the only son needed to be moved.
*/
standin->rb_nodes[standin_other] = self->rb_nodes[standin_other];
RB_SET_FATHER(standin->rb_nodes[standin_other], standin);
/*
* Now copy the result of self to standin and then replace
* self with standin in the tree.
*/
RB_COPY_PROPERTIES(standin, self);
RB_SET_FATHER(standin, RB_FATHER(self));
RB_FATHER(standin)->rb_nodes[RB_POSITION(standin)] = standin;
if (rebalance)
__archive_rb_tree_removal_rebalance(rbt, standin_father, standin_which);
}
/*
* We could do this by doing
* __archive_rb_tree_node_swap(rbt, self, which);
* __archive_rb_tree_prune_node(rbt, self, F);
*
* But it's more efficient to just evaluate and recolor the child.
*/
static void
__archive_rb_tree_prune_blackred_branch(
struct archive_rb_node *self, unsigned int which)
{
struct archive_rb_node *father = RB_FATHER(self);
struct archive_rb_node *son = self->rb_nodes[which];
/*
* Remove ourselves from the tree and give our former child our
* properties (position, color, root).
*/
RB_COPY_PROPERTIES(son, self);
father->rb_nodes[RB_POSITION(son)] = son;
RB_SET_FATHER(son, father);
}
/*
*
*/
void
__archive_rb_tree_remove_node(struct archive_rb_tree *rbt,
struct archive_rb_node *self)
{
struct archive_rb_node *standin;
unsigned int which;
/*
* In the following diagrams, we (the node to be removed) are S. Red
* nodes are lowercase. T could be either red or black.
*
* Remember the major axiom of the red-black tree: the number of
* black nodes from the root to each leaf is constant across all
* leaves, only the number of red nodes varies.
*
* Thus removing a red leaf doesn't require any other changes to a
* red-black tree. So if we must remove a node, attempt to rearrange
* the tree so we can remove a red node.
*
* The simplest case is a childless red node or a childless root node:
*
* | T --> T | or | R --> * |
* | s --> * |
*/
if (RB_CHILDLESS_P(self)) {
const int rebalance = RB_BLACK_P(self) && !RB_ROOT_P(rbt, self);
__archive_rb_tree_prune_node(rbt, self, rebalance);
return;
}
if (!RB_TWOCHILDREN_P(self)) {
/*
* The next simplest case is the node we are deleting is
* black and has one red child.
*
* | T --> T --> T |
* | S --> R --> R |
* | r --> s --> * |
*/
which = RB_LEFT_SENTINEL_P(self) ? RB_DIR_RIGHT : RB_DIR_LEFT;
__archive_rb_tree_prune_blackred_branch(self, which);
return;
}
/*
* We invert these because we prefer to remove from the inside of
* the tree.
*/
which = RB_POSITION(self) ^ RB_DIR_OTHER;
/*
* Let's find the node closes to us opposite of our parent
* Now swap it with ourself, "prune" it, and rebalance, if needed.
*/
standin = __archive_rb_tree_iterate(rbt, self, which);
__archive_rb_tree_swap_prune_and_rebalance(rbt, self, standin);
}
static void
__archive_rb_tree_removal_rebalance(struct archive_rb_tree *rbt,
struct archive_rb_node *parent, unsigned int which)
{
while (RB_BLACK_P(parent->rb_nodes[which])) {
unsigned int other = which ^ RB_DIR_OTHER;
struct archive_rb_node *brother = parent->rb_nodes[other];
if (brother == NULL)
return;/* The tree may be broken. */
/*
* For cases 1, 2a, and 2b, our brother's children must
* be black and our father must be black
*/
if (RB_BLACK_P(parent)
&& RB_BLACK_P(brother->rb_left)
&& RB_BLACK_P(brother->rb_right)) {
if (RB_RED_P(brother)) {
/*
* Case 1: Our brother is red, swap its
* position (and colors) with our parent.
* This should now be case 2b (unless C or E
* has a red child which is case 3; thus no
* explicit branch to case 2b).
*
* B -> D
* A d -> b E
* C E -> A C
*/
__archive_rb_tree_reparent_nodes(parent, other);
brother = parent->rb_nodes[other];
if (brother == NULL)
return;/* The tree may be broken. */
} else {
/*
* Both our parent and brother are black.
* Change our brother to red, advance up rank
* and go through the loop again.
*
* B -> *B
* *A D -> A d
* C E -> C E
*/
RB_MARK_RED(brother);
if (RB_ROOT_P(rbt, parent))
return; /* root == parent == black */
which = RB_POSITION(parent);
parent = RB_FATHER(parent);
continue;
}
}
/*
* Avoid an else here so that case 2a above can hit either
* case 2b, 3, or 4.
*/
if (RB_RED_P(parent)
&& RB_BLACK_P(brother)
&& RB_BLACK_P(brother->rb_left)
&& RB_BLACK_P(brother->rb_right)) {
/*
* We are black, our father is red, our brother and
* both nephews are black. Simply invert/exchange the
* colors of our father and brother (to black and red
* respectively).
*
* | f --> F |
* | * B --> * b |
* | N N --> N N |
*/
RB_MARK_BLACK(parent);
RB_MARK_RED(brother);
break; /* We're done! */
} else {
/*
* Our brother must be black and have at least one
* red child (it may have two).
*/
if (RB_BLACK_P(brother->rb_nodes[other])) {
/*
* Case 3: our brother is black, our near
* nephew is red, and our far nephew is black.
* Swap our brother with our near nephew.
* This result in a tree that matches case 4.
* (Our father could be red or black).
*
* | F --> F |
* | x B --> x B |
* | n --> n |
*/
__archive_rb_tree_reparent_nodes(brother, which);
brother = parent->rb_nodes[other];
}
/*
* Case 4: our brother is black and our far nephew
* is red. Swap our father and brother locations and
* change our far nephew to black. (these can be
* done in either order so we change the color first).
* The result is a valid red-black tree and is a
* terminal case. (again we don't care about the
* father's color)
*
* If the father is red, we will get a red-black-black
* tree:
* | f -> f --> b |
* | B -> B --> F N |
* | n -> N --> |
*
* If the father is black, we will get an all black
* tree:
* | F -> F --> B |
* | B -> B --> F N |
* | n -> N --> |
*
* If we had two red nephews, then after the swap,
* our former father would have a red grandson.
*/
if (brother->rb_nodes[other] == NULL)
return;/* The tree may be broken. */
RB_MARK_BLACK(brother->rb_nodes[other]);
__archive_rb_tree_reparent_nodes(parent, other);
break; /* We're done! */
}
}
}
struct archive_rb_node *
__archive_rb_tree_iterate(struct archive_rb_tree *rbt,
struct archive_rb_node *self, const unsigned int direction)
{
const unsigned int other = direction ^ RB_DIR_OTHER;
if (self == NULL) {
self = rbt->rbt_root;
if (RB_SENTINEL_P(self))
return NULL;
while (!RB_SENTINEL_P(self->rb_nodes[direction]))
self = self->rb_nodes[direction];
return self;
}
/*
* We can't go any further in this direction. We proceed up in the
* opposite direction until our parent is in direction we want to go.
*/
if (RB_SENTINEL_P(self->rb_nodes[direction])) {
while (!RB_ROOT_P(rbt, self)) {
if (other == (unsigned int)RB_POSITION(self))
return RB_FATHER(self);
self = RB_FATHER(self);
}
return NULL;
}
/*
* Advance down one in current direction and go down as far as possible
* in the opposite direction.
*/
self = self->rb_nodes[direction];
while (!RB_SENTINEL_P(self->rb_nodes[other]))
self = self->rb_nodes[other];
return self;
}