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_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 (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" 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。