Linux内核的红黑树RB_TREE和FreeBSD 8.0里面的AVL

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

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_BLACK 1

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

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;

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”

void my_insert(struct rb_root *root, void *ins);

int my_cmp(void *src, void *dest);

void my_rb_walk(const struct rb_root *root);

void my_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_BLACK 1

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。

Linux内核的红黑树RB_TREE和FreeBSD 8.0里面的AVL_TREE比较

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