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Translated Data Structures in the Linux Kernel
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【Translating By cposture 2016-02-26】
Data Structures in the Linux Kernel
================================================================================
Radix tree
--------------------------------------------------------------------------------
As you already know linux kernel provides many different libraries and functions which implement different data structures and algorithms. In this part we will consider one of these data structures - [Radix tree](http://en.wikipedia.org/wiki/Radix_tree). There are two files which are related to `radix tree` implementation and API in the linux kernel:
* [include/linux/radix-tree.h](https://github.com/torvalds/linux/blob/master/include/linux/radix-tree.h)
* [lib/radix-tree.c](https://github.com/torvalds/linux/blob/master/lib/radix-tree.c)
Lets talk about what a `radix tree` is. Radix tree is a `compressed trie` where a [trie](http://en.wikipedia.org/wiki/Trie) is a data structure which implements an interface of an associative array and allows to store values as `key-value`. The keys are usually strings, but any data type can be used. A trie is different from an `n-tree` because of its nodes. Nodes of a trie do not store keys; instead, a node of a trie stores single character labels. The key which is related to a given node is derived by traversing from the root of the tree to this node. For example:
```
               +-----------+
               |           |
               |    " "    |
| |
        +------+-----------+------+
        |                         |
        |                         |
   +----v------+            +-----v-----+
   |           |            |           |
   |    g      |            |     c     |
| | | |
   +-----------+            +-----------+
        |                         |
        |                         |
   +----v------+            +-----v-----+
   |           |            |           |
   |    o      |            |     a     |
| | | |
   +-----------+            +-----------+
                                  |
                                  |
                            +-----v-----+
                            |           |
                            |     t     |
| |
                            +-----------+
```
So in this example, we can see the `trie` with keys, `go` and `cat`. The compressed trie or `radix tree` differs from `trie` in that all intermediates nodes which have only one child are removed.
Radix tree in linux kernel is the datastructure which maps values to integer keys. It is represented by the following structures from the file [include/linux/radix-tree.h](https://github.com/torvalds/linux/blob/master/include/linux/radix-tree.h):
```C
struct radix_tree_root {
unsigned int height;
gfp_t gfp_mask;
struct radix_tree_node __rcu *rnode;
};
```
This structure presents the root of a radix tree and contains three fields:
* `height` - height of the tree;
* `gfp_mask` - tells how memory allocations will be performed;
* `rnode` - pointer to the child node.
The first field we will discuss is `gfp_mask`:
Low-level kernel memory allocation functions take a set of flags as - `gfp_mask`, which describes how that allocation is to be performed. These `GFP_` flags which control the allocation process can have following values: (`GF_NOIO` flag) means sleep and wait for memory, (`__GFP_HIGHMEM` flag) means high memory can be used, (`GFP_ATOMIC` flag) means the allocation process has high-priority and can't sleep etc.
* `GFP_NOIO` - can sleep and wait for memory;
* `__GFP_HIGHMEM` - high memory can be used;
* `GFP_ATOMIC` - allocation process is high-priority and can't sleep;
etc.
The next field is `rnode`:
```C
struct radix_tree_node {
unsigned int path;
unsigned int count;
union {
struct {
struct radix_tree_node *parent;
void *private_data;
};
struct rcu_head rcu_head;
};
/* For tree user */
struct list_head private_list;
void __rcu *slots[RADIX_TREE_MAP_SIZE];
unsigned long tags[RADIX_TREE_MAX_TAGS][RADIX_TREE_TAG_LONGS];
};
```
This structure contains information about the offset in a parent and height from the bottom, count of the child nodes and fields for accessing and freeing a node. This fields are described below:
* `path` - offset in parent & height from the bottom;
* `count` - count of the child nodes;
* `parent` - pointer to the parent node;
* `private_data` - used by the user of a tree;
* `rcu_head` - used for freeing a node;
* `private_list` - used by the user of a tree;
The two last fields of the `radix_tree_node` - `tags` and `slots` are important and interesting. Every node can contains a set of slots which are store pointers to the data. Empty slots in the linux kernel radix tree implementation store `NULL`. Radix trees in the linux kernel also supports tags which are associated with the `tags` fields in the `radix_tree_node` structure. Tags allow individual bits to be set on records which are stored in the radix tree.
Now that we know about radix tree structure, it is time to look on its API.
Linux kernel radix tree API
---------------------------------------------------------------------------------
We start from the datastructure initialization. There are two ways to initialize a new radix tree. The first is to use `RADIX_TREE` macro:
```C
RADIX_TREE(name, gfp_mask);
````
As you can see we pass the `name` parameter, so with the `RADIX_TREE` macro we can define and initialize radix tree with the given name. Implementation of the `RADIX_TREE` is easy:
```C
#define RADIX_TREE(name, mask) \
struct radix_tree_root name = RADIX_TREE_INIT(mask)
#define RADIX_TREE_INIT(mask) { \
.height = 0, \
.gfp_mask = (mask), \
.rnode = NULL, \
}
```
At the beginning of the `RADIX_TREE` macro we define instance of the `radix_tree_root` structure with the given name and call `RADIX_TREE_INIT` macro with the given mask. The `RADIX_TREE_INIT` macro just initializes `radix_tree_root` structure with the default values and the given mask.
The second way is to define `radix_tree_root` structure by hand and pass it with mask to the `INIT_RADIX_TREE` macro:
```C
struct radix_tree_root my_radix_tree;
INIT_RADIX_TREE(my_tree, gfp_mask_for_my_radix_tree);
```
where:
```C
#define INIT_RADIX_TREE(root, mask) \
do { \
(root)->height = 0; \
(root)->gfp_mask = (mask); \
(root)->rnode = NULL; \
} while (0)
```
makes the same initialziation with default values as it does `RADIX_TREE_INIT` macro.
The next are two functions for inserting and deleting records to/from a radix tree:
* `radix_tree_insert`;
* `radix_tree_delete`;
The first `radix_tree_insert` function takes three parameters:
* root of a radix tree;
* index key;
* data to insert;
The `radix_tree_delete` function takes the same set of parameters as the `radix_tree_insert`, but without data.
The search in a radix tree implemented in two ways:
* `radix_tree_lookup`;
* `radix_tree_gang_lookup`;
* `radix_tree_lookup_slot`.
The first `radix_tree_lookup` function takes two parameters:
* root of a radix tree;
* index key;
This function tries to find the given key in the tree and return the record associated with this key. The second `radix_tree_gang_lookup` function have the following signature
```C
unsigned int radix_tree_gang_lookup(struct radix_tree_root *root,
void **results,
unsigned long first_index,
unsigned int max_items);
```
and returns number of records, sorted by the keys, starting from the first index. Number of the returned records will not be greater than `max_items` value.
And the last `radix_tree_lookup_slot` function will return the slot which will contain the data.
Links
---------------------------------------------------------------------------------
* [Radix tree](http://en.wikipedia.org/wiki/Radix_tree)
* [Trie](http://en.wikipedia.org/wiki/Trie)
--------------------------------------------------------------------------------
via: https://github.com/0xAX/linux-insides/edit/master/DataStructures/radix-tree.md
作者：[0xAX]
译者：[译者ID](https://github.com/译者ID)
校对：[校对者ID](https://github.com/校对者ID)
本文由 [LCTT](https://github.com/LCTT/TranslateProject) 原创翻译，[Linux中国](http://linux.cn/) 荣誉推出

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Linux内核数据结构
================================================================================
基数树 Radix tree
--------------------------------------------------------------------------------
正如你所知道的，Linux内核提供了许多不同的库和函数，它们实现了不同的数据结构和算法。在这部分，我们将研究其中一种数据结构——[基数树 Radix tree](http://en.wikipedia.org/wiki/Radix_tree)。在Linux内核中，有两个与基数树实现和API相关的文件：
* [include/linux/radix-tree.h](https://github.com/torvalds/linux/blob/master/include/linux/radix-tree.h)
* [lib/radix-tree.c](https://github.com/torvalds/linux/blob/master/lib/radix-tree.c)
让我们讨论什么是`基数树`吧。基数树是一种`压缩的字典树`，而[字典树](http://en.wikipedia.org/wiki/Trie)是实现了关联数组接口并允许以`键值对`方式存储值的一种数据结构。该键通常是字符串，但能够使用任何数据类型。字典树因为它的节点而与`n叉树`不同。字典树的节点不存储键；相反，字典树的一个节点存储单个字符的标签。与一个给定节点关联的键可以通过从根遍历到该节点获得。举个例子：
```
               +-----------+
               |           |
               |    " "    |
| |
        +------+-----------+------+
        |                         |
        |                         |
   +----v------+            +-----v-----+
   |           |            |           |
   |    g      |            |     c     |
| | | |
   +-----------+            +-----------+
        |                         |
        |                         |
   +----v------+            +-----v-----+
   |           |            |           |
   |    o      |            |     a     |
| | | |
   +-----------+            +-----------+
                                  |
                                  |
                            +-----v-----+
                            |           |
                            |     t     |
| |
                            +-----------+
```
因此在这个例子中，我们可以看到一个有着两个键`go`和`cat`的`字典树`。压缩的字典树或者`基数树`和`字典树`不同于所有只有一个孩子的中间节点都被删除。
Linu内核中的基数树是映射值到整形键的一种数据结构。[include/linux/radix-tree.h](https://github.com/torvalds/linux/blob/master/include/linux/radix-tree.h)文件中的以下结构体表示了基数树：
```C
struct radix_tree_root {
unsigned int height;
gfp_t gfp_mask;
struct radix_tree_node __rcu *rnode;
};
```
这个结构体表示了一个基数树的根，并包含了3个域成员：
* `height` - 树的高度;
* `gfp_mask` - 告诉如何执行动态内存分配;
* `rnode` - 孩子节点指针.
我们第一个要讨论的域是`gfp_mask`：
底层内核内存动态分配函数以一组标志作为` gfp_mask `，用于描述如何执行动态内存分配。这些控制分配进程的`GFP_`标志拥有以下值：(`GF_NOIO`标志)意味着睡眠等待内存，(`__GFP_HIGHMEM`标志)意味着高端内存能够被使用，(`GFP_ATOMIC`标志)意味着分配进程拥有高优先级并不能睡眠等等。
* `GFP_NOIO` - 睡眠等待内存
* `__GFP_HIGHMEM` - 高端内存能够被使用;
* `GFP_ATOMIC` - 分配进程拥有高优先级并且不能睡眠;
等等。
下一个域是`rnode`：
```C
struct radix_tree_node {
unsigned int path;
unsigned int count;
union {
struct {
struct radix_tree_node *parent;
void *private_data;
};
struct rcu_head rcu_head;
};
/* For tree user */
struct list_head private_list;
void __rcu *slots[RADIX_TREE_MAP_SIZE];
unsigned long tags[RADIX_TREE_MAX_TAGS][RADIX_TREE_TAG_LONGS];
};
```
这个结构体包含的信息有父节点中的偏移以及到底端(叶节点)的高度、孩子节点的个数以及用于访问和释放节点的域成员。这些域成员描述如下：
* `path` - 父节点中的偏移和到底端(叶节点)的高度
* `count` - 孩子节点的个数;
* `parent` - 父节点指针;
* `private_data` - 由树的用户使用;
* `rcu_head` - 用于释放节点;
* `private_list` - 由树的用户使用;
`radix_tree_node`的最后两个成员——`tags`和`slots`非常重要且令人关注。Linux内核基数树的每个节点都包含一组存储指向数据指针的slots。Linux内核基数树实现的空slots存储`NULL`值。Linux内核中的基数树也支持与`radix_tree_node`结构体的`tags`域相关联的标签。标签允许在基数树存储的记录中设置各个位。
既然我们了解了基数树的结构，那么该是时候看一下它的API了。
Linux内核基数树API
---------------------------------------------------------------------------------
我们从结构体的初始化开始。有两种方法初始化一个新的基数树。第一种是使用`RADIX_TREE`宏：
```C
RADIX_TREE(name, gfp_mask);
````
正如你所看到的，我们传递`name`参数，所以使用`RADIX_TREE`宏，我们能够定义和初始化基数树为给定的名字。`RADIX_TREE`的实现是简单的：
```C
#define RADIX_TREE(name, mask) \
struct radix_tree_root name = RADIX_TREE_INIT(mask)
#define RADIX_TREE_INIT(mask) { \
.height = 0, \
.gfp_mask = (mask), \
.rnode = NULL, \
}
```
在`RADIX_TREE`宏的开始，我们使用给定的名字定义`radix_tree_root`结构体实例，并使用给定的mask调用`RADIX_TREE_INIT`宏。`RADIX_TREE_INIT`宏只是初始化`radix_tree_root`结构体为默认值和给定的mask而已。
第二种方法是亲手定义`radix_tree_root`结构体，并且将它和mask传给`INIT_RADIX_TREE`宏：
```C
struct radix_tree_root my_radix_tree;
INIT_RADIX_TREE(my_tree, gfp_mask_for_my_radix_tree);
```
where:
```C
#define INIT_RADIX_TREE(root, mask) \
do { \
(root)->height = 0; \
(root)->gfp_mask = (mask); \
(root)->rnode = NULL; \
} while (0)
```
和`RADIX_TREE_INIT`宏所做的初始化一样，初始化为默认值。
接下来是用于从基数树插入和删除数据的两个函数：
* `radix_tree_insert`;
* `radix_tree_delete`;
第一个函数`radix_tree_insert`需要3个参数：
* 基数树的根;
* 索引键;
* 插入的数据;
`radix_tree_delete`函数需要和`radix_tree_insert`一样的一组参数，但是没有data。
基数树的搜索以两种方法实现：
* `radix_tree_lookup`;
* `radix_tree_gang_lookup`;
* `radix_tree_lookup_slot`.
第一个函数`radix_tree_lookup`需要两个参数：
* 基数树的根;
* 索引键;
这个函数尝试在树中查找给定的键，并返回和该键相关联的记录。第二个函数`radix_tree_gang_lookup`有以下的函数签名：
```C
unsigned int radix_tree_gang_lookup(struct radix_tree_root *root,
void **results,
unsigned long first_index,
unsigned int max_items);
```
和返回记录的个数，(results指向的数据)按键排序并从第一个索引开始。返回的记录个数将不会超过`max_items`。
最后一个函数`radix_tree_lookup_slot`将会返回包含数据的slot。
链接
---------------------------------------------------------------------------------
* [Radix tree](http://en.wikipedia.org/wiki/Radix_tree)
* [Trie](http://en.wikipedia.org/wiki/Trie)
--------------------------------------------------------------------------------
via: https://github.com/0xAX/linux-insides/edit/master/DataStructures/radix-tree.md
作者：[0xAX]
译者：[cposture](https://github.com/cposture)
校对：[校对者ID](https://github.com/校对者ID)
本文由 [LCTT](https://github.com/LCTT/TranslateProject) 原创翻译，[Linux中国](http://linux.cn/) 荣誉推出