Linux内核的红黑树RB_TREE和FreeBSD 8.0里面的AVL_TREE比较之一 RB_TREE
这里不涉及到avl树和红黑树谁优谁劣，只是谈谈在两种实现的一些细节，以及最后给出一些性能比较。
这里先给出Linux下面的红黑树的实现，因为Linux下面的两个宏定义不好直接使用，原型如下：
#define rb_entry(ptr, type, member) container_of(ptr, type, member)
#ifndef container_of
/**
* container_of - cast a member of a structure out to the containing structure
* @ptr:the pointer to the member.
* @type: the type of the container struct this is embedded in.
* @member: the name of the member within the struct.
*
*/
#define container_of(ptr, type, member) ({ \
const typeof(((type *)0)->member) * __mptr = (ptr); \
(type *)((char *)__mptr - offsetof(type, member)); })
#endif
#ifndef offsetof
#define offsetof(TYPE, MEMBER) ((size_t) &((TYPE *)0)->MEMBER)
#endif
修改如下：
#ifndef offsetof
#define offsetof(TYPE, MEMBER) ((size_t) &((TYPE *)0)->MEMBER)
#endif
#ifndef container_of
/**
* container_of - cast a member of a structure out to the containing structure
* @ptr:the pointer to the member.
* @type: the type of the container struct this is embedded in.
* @member: the name of the member within the struct.
*
* !!! modify the typeof marco, just use the rb_node
*/
#define container_of(ptr, type, member) \
(((char *)ptr) - offsetof(type, member))
#endif
#define rb_entry(ptr, type, member) container_of(ptr, type, member)
语义可以认为不变的。
linux的RB_TREE源代码移植到vc上后，命名为：rb_tree.h， 如下：
/*
Red Black Trees
(C) 1999 Andrea Arcangeli <andrea@SUSE.de>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
linux/include/linux/rbtree.h
To use rbtrees you'll have to implement your own insert and search cores.
This will avoid us to use callbacks and to drop drammatically performances.
I know it's not the cleaner way, but in C (not in C++) to get
performances and genericity...
Some example of insert and search follows here. The search is a plain
normal search over an ordered tree. The insert instead must be implemented
in two steps: First, the code must insert the element in order as a red leaf
in the tree, and then the support library function rb_insert_color() must
be called. Such function will do the not trivial work to rebalance the
rbtree, if necessary.
-----------------------------------------------------------------------
static inline struct page * rb_search_page_cache(struct inode * inode,
unsigned long offset)
{
struct rb_node * n = inode->i_rb_page_cache.rb_node;
struct page * page;
while (n)
{
page = rb_entry(n, struct page, rb_page_cache);
if (offset < page->offset)
n = n->rb_left;
else if (offset > page->offset)
n = n->rb_right;
else
return page;
}
return NULL;
}
static inline struct page * __rb_insert_page_cache(struct inode * inode,
unsigned long offset,
struct rb_node * node)
{
struct rb_node ** p = &inode->i_rb_page_cache.rb_node;
struct rb_node * parent = NULL;
struct page * page;
while (*p)
{
parent = *p;
page = rb_entry(parent, struct page, rb_page_cache);
if (offset < page->offset)
p = &(*p)->rb_left;
else if (offset > page->offset)
p = &(*p)->rb_right;
else
return page;
}
rb_link_node(node, parent, p);
return NULL;
}
static inline struct page * rb_insert_page_cache(struct inode * inode,
unsigned long offset,
struct rb_node * node)
{
struct page * ret;
if ((ret = __rb_insert_page_cache(inode, offset, node)))
goto out;
rb_insert_color(node, &inode->i_rb_page_cache);
out:
return ret;
}
-----------------------------------------------------------------------
*/
#ifndef _LINUX_RBTREE_H
#define _LINUX_RBTREE_H
#define EXPORT_SYMBOL(i)
#pragma pack (push)
#pragma pack(4)
struct rb_node
{
unsigned long rb_parent_color;
#define RB_RED 0
#define RB_BLACK1
struct rb_node *rb_right;
struct rb_node *rb_left;
} ;
#pragma pack (pop)
/* The alignment might seem pointless, but allegedly CRIS needs it */
struct rb_root
{
struct rb_node *rb_node;
int (*cmp)(void *src, void *dst);
void(*insert)(struct rb_root *root, void *ins);
void(*remove)(struct rb_root *root, void *del);
};
#define rb_parent(r) ((struct rb_node *)((r)->rb_parent_color & ~3))
#define rb_color(r) ((r)->rb_parent_color & 1)
#define rb_is_red(r) (!rb_color(r))
#define rb_is_black(r) rb_color(r)
#define rb_set_red(r) do { (r)->rb_parent_color &= ~1; } while (0)
#define rb_set_black(r) do { (r)->rb_parent_color |= 1; } while (0)
static inline void rb_set_parent(struct rb_node *rb, struct rb_node *p)
{
rb->rb_parent_color = (rb->rb_parent_color & 3) | (unsigned long)p;
}
static inline void rb_set_color(struct rb_node *rb, int color)
{
rb->rb_parent_color = (rb->rb_parent_color & ~1) | color;
}
#ifndef offsetof
#define offsetof(TYPE, MEMBER) ((size_t) &((TYPE *)0)->MEMBER)
#endif
#ifndef container_of
/**
* container_of - cast a member of a structure out to the containing structure
* @ptr:the pointer to the member.
* @type: the type of the container struct this is embedded in.
* @member: the name of the member within the struct.
*
* !!! modify the typeof marco, just use the rb_node
*/
#define container_of(ptr, type, member) \
(((char *)ptr) - offsetof(type, member))
#endif
#define RB_ROOT (struct rb_root) { NULL, }
#define rb_entry(ptr, type, member) container_of(ptr, type, member)
#define RB_EMPTY_ROOT(root) ((root)->rb_node == NULL)
#define RB_EMPTY_NODE(node) (rb_parent(node) == node)
#define RB_CLEAR_NODE(node) (rb_set_parent(node, node))
static inline void rb_init_node(struct rb_node *rb)
{
rb->rb_parent_color = 0;
rb->rb_right = NULL;
rb->rb_left = NULL;
RB_CLEAR_NODE(rb);
}
extern void rb_insert_color(struct rb_node *, struct rb_root *);
extern void rb_erase(struct rb_node *, struct rb_root *);
typedef void (*rb_augment_f)(struct rb_node *node, void *data);
extern void rb_augment_insert(struct rb_node *node,
rb_augment_f func, void *data);
extern struct rb_node *rb_augment_erase_begin(struct rb_node *node);
extern void rb_augment_erase_end(struct rb_node *node,
rb_augment_f func, void *data);
/* Find logical next and previous nodes in a tree */
extern struct rb_node *rb_next(const struct rb_node *);
extern struct rb_node *rb_prev(const struct rb_node *);
extern struct rb_node *rb_first(const struct rb_root *);
extern struct rb_node *rb_last(const struct rb_root *);
/* Fast replacement of a single node without remove/rebalance/add/rebalance */
extern void rb_replace_node(struct rb_node *victim, struct rb_node *new_node_node,
struct rb_root *root);
static inline void rb_link_node(struct rb_node * node, struct rb_node * parent,
struct rb_node ** rb_link)
{
node->rb_parent_color = (unsigned long )parent;
node->rb_left = node->rb_right = NULL;
*rb_link = node;
}
#endif /* _LINUX_RBTREE_H */
实现文件移植之后，命名为rb_tree.cpp， 如下：
/*
Red Black Trees
(C) 1999 Andrea Arcangeli <andrea@SUSE.de>
(C) 2002 David Woodhouse <dwmw2@infradead.org>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
linux/lib/rbtree.c
*/
#include "rb_tree.h"
static void __rb_rotate_left(struct rb_node *node, struct rb_root *root)
{
struct rb_node *right = node->rb_right;
struct rb_node *parent = rb_parent(node);
if ((node->rb_right = right->rb_left))
rb_set_parent(right->rb_left, node);
right->rb_left = node;
rb_set_parent(right, parent);
if (parent)
{
if (node == parent->rb_left)
parent->rb_left = right;
else
parent->rb_right = right;
}
else
root->rb_node = right;
rb_set_parent(node, right);
}
static void __rb_rotate_right(struct rb_node *node, struct rb_root *root)
{
struct rb_node *left = node->rb_left;
struct rb_node *parent = rb_parent(node);
if ((node->rb_left = left->rb_right))
rb_set_parent(left->rb_right, node);
left->rb_right = node;
rb_set_parent(left, parent);
if (parent)
{
if (node == parent->rb_right)
parent->rb_right = left;
else
parent->rb_left = left;
}
else
root->rb_node = left;
rb_set_parent(node, left);
}
void rb_insert_color(struct rb_node *node, struct rb_root *root)
{
struct rb_node *parent, *gparent;
while ((parent = rb_parent(node)) && rb_is_red(parent))
{
gparent = rb_parent(parent);
if (parent == gparent->rb_left)
{
{
register struct rb_node *uncle = gparent->rb_right;
if (uncle && rb_is_red(uncle))
{
rb_set_black(uncle);
rb_set_black(parent);
rb_set_red(gparent);
node = gparent;
continue;
}
}
if (parent->rb_right == node)
{
register struct rb_node *tmp;
__rb_rotate_left(parent, root);
tmp = parent;
parent = node;
node = tmp;
}
rb_set_black(parent);
rb_set_red(gparent);
__rb_rotate_right(gparent, root);
} else {
{
register struct rb_node *uncle = gparent->rb_left;
if (uncle && rb_is_red(uncle))
{
rb_set_black(uncle);
rb_set_black(parent);
rb_set_red(gparent);
node = gparent;
continue;
}
}
if (parent->rb_left == node)
{
register struct rb_node *tmp;
__rb_rotate_right(parent, root);
tmp = parent;
parent = node;
node = tmp;
}
rb_set_black(parent);
rb_set_red(gparent);
__rb_rotate_left(gparent, root);
}
}
rb_set_black(root->rb_node);
}
EXPORT_SYMBOL(rb_insert_color);
static void __rb_erase_color(struct rb_node *node, struct rb_node *parent,
struct rb_root *root)
{
struct rb_node *other;
while ((!node || rb_is_black(node)) && node != root->rb_node)
{
if (parent->rb_left == node)
{
other = parent->rb_right;
if (rb_is_red(other))
{
rb_set_black(other);
rb_set_red(parent);
__rb_rotate_left(parent, root);
other = parent->rb_right;
}
if ((!other->rb_left || rb_is_black(other->rb_left)) &&
(!other->rb_right || rb_is_black(other->rb_right)))
{
rb_set_red(other);
node = parent;
parent = rb_parent(node);
}
else
{
if (!other->rb_right || rb_is_black(other->rb_right))
{
rb_set_black(other->rb_left);
rb_set_red(other);
__rb_rotate_right(other, root);
other = parent->rb_right;
}
rb_set_color(other, rb_color(parent));
rb_set_black(parent);
rb_set_black(other->rb_right);
__rb_rotate_left(parent, root);
node = root->rb_node;
break;
}
}
else
{
other = parent->rb_left;
if (rb_is_red(other))
{
rb_set_black(other);
rb_set_red(parent);
__rb_rotate_right(parent, root);
other = parent->rb_left;
}
if ((!other->rb_left || rb_is_black(other->rb_left)) &&
(!other->rb_right || rb_is_black(other->rb_right)))
{
rb_set_red(other);
node = parent;
parent = rb_parent(node);
}
else
{
if (!other->rb_left || rb_is_black(other->rb_left))
{
rb_set_black(other->rb_right);
rb_set_red(other);
__rb_rotate_left(other, root);
other = parent->rb_left;
}
rb_set_color(other, rb_color(parent));
rb_set_black(parent);
rb_set_black(other->rb_left);
__rb_rotate_right(parent, root);
node = root->rb_node;
break;
}
}
}
if (node)
rb_set_black(node);
}
void rb_erase(struct rb_node *node, struct rb_root *root)
{
struct rb_node *child, *parent;
int color;
if (!node->rb_left)
child = node->rb_right;
else if (!node->rb_right)
child = node->rb_left;
else
{
struct rb_node *old = node, *left;
node = node->rb_right;
while ((left = node->rb_left) != NULL)
node = left;
if (rb_parent(old)) {
if (rb_parent(old)->rb_left == old)
rb_parent(old)->rb_left = node;
else
rb_parent(old)->rb_right = node;
} else
root->rb_node = node;
child = node->rb_right;
parent = rb_parent(node);
color = rb_color(node);
if (parent == old) {
parent = node;
} else {
if (child)
rb_set_parent(child, parent);
parent->rb_left = child;
node->rb_right = old->rb_right;
rb_set_parent(old->rb_right, node);
}
node->rb_parent_color = old->rb_parent_color;
node->rb_left = old->rb_left;
rb_set_parent(old->rb_left, node);
goto color;
}
parent = rb_parent(node);
color = rb_color(node);
if (child)
rb_set_parent(child, parent);
if (parent)
{
if (parent->rb_left == node)
parent->rb_left = child;
else
parent->rb_right = child;
}
else
root->rb_node = child;
color:
if (color == RB_BLACK)
__rb_erase_color(child, parent, root);
}
EXPORT_SYMBOL(rb_erase);
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_node 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_parent(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_parent(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_node,
struct rb_root *root)
{
struct rb_node *parent = rb_parent(victim);
/* Set the surrounding nodes to point to the replacement */
if (parent) {
if (victim == parent->rb_left)
parent->rb_left = new_node;
else
parent->rb_right = new_node;
} else {
root->rb_node = new_node;
}
if (victim->rb_left)
rb_set_parent(victim->rb_left, new_node);
if (victim->rb_right)
rb_set_parent(victim->rb_right, new_node);
/* Copy the pointers/colour from the victim to the replacement */
*new_node = *victim;
}
EXPORT_SYMBOL(rb_replace_node);
其实，可以看出，linux内核里面并没有提供直接可以用的insert delete 以及walk遍历的函数接口，linux提供的是最基本一个插入节点后的re-fixup，删除后的re-fixup，以及walk需要的get-firt, get-next等等。
这里是需要自己提供插入，删除，以及walk函数的，相比freebsd的avl树，完全就是一步到位了，而且好用很多，这里不谈谁好用，然后举例简单说说怎么使用linux的基本的这些函数，晚点会比较二者在插入删除以及walk方面的优劣。
自己提供相应的一些接口了，时间有限随便写写：
应用头文件，rb_tree_main.h：
#ifndef RB_TREE_MAIN_H
#define RB_TREE_MAIN_H
#include "rb_tree.h"
voidmy_insert(struct rb_root *root, void *ins);
int my_cmp(void *src, void *dest);
voidmy_rb_walk(const struct rb_root *root);
voidmy_remove(struct rb_root *g_my_root, void *del);
#endif
man文件：rb_tree_main.cpp
// rb_tree_main.cpp : Defines the entry point for the console application.
//
#include <string.h>
#include <stdlib.h>
#include "rb_tree.h"
#include "rb_tree_main.h"
typedef struct my_rb
{
int rand_val;
struct rb_node my_rb_node;
}my_rb;
struct rb_root g_my_root = {NULL, my_cmp, my_insert, my_remove};
void my_insert(struct rb_root *root, void *ins)
{
struct my_rb *iter;
struct my_rb *src = (struct my_rb *)ins;
struct rb_node **p = &root->rb_node;
struct rb_node *parent = NULL;
if(!ins)
{
return;
}
while (*p != NULL) {
parent = *p;
iter = (struct my_rb *)rb_entry(parent, struct my_rb, my_rb_node);
if (root->cmp(src, iter) < 0)
p = &(*p)->rb_left;
else
p = &(*p)->rb_right;
}
rb_link_node(&src->my_rb_node, parent, p);
rb_insert_color(&src->my_rb_node, root);
}
int my_cmp(void *src, void *dest)
{
struct my_rb *my_src = (struct my_rb *)src;
struct my_rb *my_dest = (struct my_rb *)dest;
if(!my_src || !my_dest)
{
return 0;
}
if(my_src->rand_val < my_dest->rand_val)
{
return -1;
}
else if(my_src->rand_val > my_dest->rand_val)
{
return 1;
}
else
{
return 0;
}
}
void my_remove(struct rb_root *g_my_root, void *del)
{
struct my_rb*entry = NULL;
struct my_rb*del_node = (struct my_rb *)del;
struct rb_node *n = NULL;
if(!g_my_root || !del)
{
return;
}
n = g_my_root->rb_node;
while (n)
{
entry = (struct my_rb *)rb_entry(n, struct my_rb, my_rb_node);
if (g_my_root->cmp(entry, del_node) > 0)
{
n = n->rb_left;
}
else if (g_my_root->cmp(entry, del_node) < 0)
{
n = n->rb_right;
}
else
{
rb_erase(n, g_my_root);
free(entry);
entry = NULL;
return ;
}
}
return ;
}
void my_rb_walk(const struct rb_root *root)
{
struct rb_node *temp = rb_first(root);
struct my_rb *my_entry = NULL;
while(temp)
{
my_entry = (struct my_rb *)rb_entry(temp, my_rb, my_rb_node);
printf("node with rand_val %d .\n", my_entry->rand_val);
temp = rb_next(temp);
}
}
int main(int argc, char* argv[])
{
struct my_rb *my_rb_node = NULL;
struct my_rb del_node = {4, {0}};
for (int i = 0; i < 5; i++)
{
my_rb_node = (struct my_rb *)malloc(sizeof *my_rb_node);
memset(my_rb_node, 0, sizeof *my_rb_node);
my_rb_node->rand_val = i;
g_my_root.insert(&g_my_root, my_rb_node);
}
my_rb_walk(&g_my_root);
g_my_root.remove(&g_my_root, &del_node);
my_rb_walk(&g_my_root);
return 0;
}
注意四点：
1、insert里面的双重指针，直接找到要插入的位置的父节点，省去了一堆赋值比如parent->left or right = p, p->parent 啥啥啥的，直接在父节点（叶子节点）的左或者右节点NULL的取一次地址，然后，地址上面写值，不细说了；
2、插入的节点应该动态分配，或者是已经静态分配好的多个节点
3、删除操作，内核提供的只是re-fixup，不会帮你释放内存的，我们要做的是找到这个节点，然后调用内核提供的rb_erase，把节点从rb树上移去，如果是动态分配，再释放之。
4、内核的红黑树是带有parent属性的，只是么有用指针，而是把parent和left和right子标记用了一个字段而已：
unsigned long rb_parent_color;
最低的一位用作了left和right的flag，最高的31位，用作存储parent指针的地址，这种rb树就要求插入的节点地址必须是偶数的，一般的cpu架构使得分配出来的内存都是偶数地址对齐的了，但是有些也会以奇数开始，比如ppc，就可能动态分配出一个节点就是从奇数地址开始的。只要是偶数地址开始那么地址的最低位一定是0了。
其实在3.0.1的内核里面是这种rb设计，在早期的内核里面rb_node就是另外一种设计了，是引入了parent指针的，比如2.6.11的内核的结构体设计如下：
struct rb_node
{
struct rb_node *rb_parent;
int rb_color;
#define RB_RED 0
#define RB_BLACK1
struct rb_node *rb_right;
struct rb_node *rb_left;
};
其实在freebsd 8.0的avl树64位设计就是这种，32二位的设计类似于早些时候的内核的rb树的节点设计：
#ifndef _LP64
struct avl_node {
struct avl_node *avl_child[2]; /* left/right children */
struct avl_node *avl_parent;/* this node's parent */
unsigned short avl_child_index; /* my index in parent's avl_child[] */
short avl_balance; /* balance value: -1, 0, +1 */
};
#else /* _LP64 */
/*
* for 64 bit machines, avl_pcb contains parent pointer, balance and child_index
* values packed in the following manner:
*
* |63 3|2|1 0 |
* |-------------------------------------|-----------------|-------------|
* | avl_parent hi order bits | avl_child_index | avl_balance |
* | | | + 1 |
* |-------------------------------------|-----------------|-------------|
*
*/
struct avl_node {
struct avl_node *avl_child[2]; /* left/right children nodes */
uintptr_t avl_pcb; /* parent, child_index, balance */
};
#endif
说这么多，以后再说freebsd的avl树咋用的吧。