diff --git a/DataStructures/radix-tree.md b/DataStructures/radix-tree.md new file mode 100644 index 0000000..d8c25e5 --- /dev/null +++ b/DataStructures/radix-tree.md @@ -0,0 +1,182 @@ +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)