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. There are two files which are related to radix tree
implementation and API in the linux kernel:
Lets talk about what a radix tree
is. Radix tree is a compressed trie
where a trie is a data structure which implements an interface of an associative array and allows to store values as keyvalue
. The keys are usually strings, but any data type can be used. A trie is different from an ntree
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 data structure which maps values to integer keys. It is represented by the following structures from the file include/linux/radixtree.h:
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
:
Lowlevel 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 highpriority 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 highpriority and can't sleep;
etc.
The next field is rnode
:
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 data structure initialization. There are two ways to initialize a new radix tree. The first is to use RADIX_TREE
macro:
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:
#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:
struct radix_tree_root my_radix_tree;
INIT_RADIX_TREE(my_tree, gfp_mask_for_my_radix_tree);
where:
#define INIT_RADIX_TREE(root, mask) \
do { \
(root)>height = 0; \
(root)>gfp_mask = (mask); \
(root)>rnode = NULL; \
} while (0)
makes the same initialization 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
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.