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Data Structures in the Linux Kernel
================================================================================
Radix tree
--------------------------------------------------------------------------------
As you alread can know linux kernel provides many different libraries and functions which implements different data structures and algorithm. 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 related with `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)
Let's talk first of all about what is it `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`. In general way keys are strings, but of course we can use any data type. Trie different from any `n-tree` in its nodes. Nodes of a trie does not store keys. Instead, node of a trie stores one-character labels and the key which related to the given node is full way from the root of a 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` that all intermediates nodes which have only one child are removed.
Radix tree in the linux kernel is mechanism which maps values to the integer key. It represented by the following structures from the [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.
Here is interesting only one field - `gfp_mask`. The low-level kernel memory allocation functions take a set of flags describing how that allocation is to be performed. These `GFP_` flags control is the allocation process can be sleep and wait for memory (`GF_NOIO` flag), is high memory can be used (`__GFP_HIGHMEM`), is allocation process high-priority and can't sleep (`GFP_ATOMIC` flag) and etc...
The next structure as you already can guess is `radix_tree_node`:
```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];
};
```
The `radix_tree_node` structure contains information about the offset in a parent and hieght from the bottom, count of the child nodes and fields for te accessing and freeing a node. `radix_tree_node` contains following fields:
* `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 contain the 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
---------------------------------------------------------------------------------
Every part about any data structure, we start from the data structure intialization. There are two way how 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 give name and call `RADIX_TREE_INIT` macro with the givin 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. They are:
* `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 give key in the tree and returns associated record with this key. The second `radix_tree_gan_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 amount of the records which are sorted by the keys starting from the first index. Amount 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)