|
|
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 is `radix tree`. Radix tree is a `compressed trie` where [trie](http://en.wikipedia.org/wiki/Trie) is a data structure which implements interface of an associative array and allows to store values as `key-value`. The keys are usually strings, but any other data type can be used as well. Trie is different from any `n-tree` in 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`, such that all intermediates nodes which have only one child are removed.
|
|
|
|
|
|
Radix tree in linux kernel is the datastructure which maps values to the integer key. 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 are to be performed;
|
|
|
* `rnode` - pointer to the child node.
|
|
|
|
|
|
The first structure 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) be sleep and wait for memory, (`__GFP_HIGHMEM` flag) is high memory can be used, (`GFP_ATOMIC` flag) is allocation process high-priority and can't sleep etc.
|
|
|
|
|
|
The next structure 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. The 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 tree in the linux kernel also supports tags which are associated with the `tags` fields in the `radix_tree_node` structure. Tags allow to set individual bits on records which are stored in the radix tree.
|
|
|
|
|
|
Now we know about radix tree structure, time to look on its API.
|
|
|
|
|
|
Linux kernel radix tree API
|
|
|
---------------------------------------------------------------------------------
|
|
|
|
|
|
We start from the datastructure intialization. There are two ways to initialize 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 the 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 returns associated record 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 be not 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)
|
