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authorAndré Fabian Silva Delgado <emulatorman@parabola.nu>2015-08-05 17:04:01 -0300
committerAndré Fabian Silva Delgado <emulatorman@parabola.nu>2015-08-05 17:04:01 -0300
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+ ========================================
+ GENERIC ASSOCIATIVE ARRAY IMPLEMENTATION
+ ========================================
+
+Contents:
+
+ - Overview.
+
+ - The public API.
+ - Edit script.
+ - Operations table.
+ - Manipulation functions.
+ - Access functions.
+ - Index key form.
+
+ - Internal workings.
+ - Basic internal tree layout.
+ - Shortcuts.
+ - Splitting and collapsing nodes.
+ - Non-recursive iteration.
+ - Simultaneous alteration and iteration.
+
+
+========
+OVERVIEW
+========
+
+This associative array implementation is an object container with the following
+properties:
+
+ (1) Objects are opaque pointers. The implementation does not care where they
+ point (if anywhere) or what they point to (if anything).
+
+ [!] NOTE: Pointers to objects _must_ be zero in the least significant bit.
+
+ (2) Objects do not need to contain linkage blocks for use by the array. This
+ permits an object to be located in multiple arrays simultaneously.
+ Rather, the array is made up of metadata blocks that point to objects.
+
+ (3) Objects require index keys to locate them within the array.
+
+ (4) Index keys must be unique. Inserting an object with the same key as one
+ already in the array will replace the old object.
+
+ (5) Index keys can be of any length and can be of different lengths.
+
+ (6) Index keys should encode the length early on, before any variation due to
+ length is seen.
+
+ (7) Index keys can include a hash to scatter objects throughout the array.
+
+ (8) The array can iterated over. The objects will not necessarily come out in
+ key order.
+
+ (9) The array can be iterated over whilst it is being modified, provided the
+ RCU readlock is being held by the iterator. Note, however, under these
+ circumstances, some objects may be seen more than once. If this is a
+ problem, the iterator should lock against modification. Objects will not
+ be missed, however, unless deleted.
+
+(10) Objects in the array can be looked up by means of their index key.
+
+(11) Objects can be looked up whilst the array is being modified, provided the
+ RCU readlock is being held by the thread doing the look up.
+
+The implementation uses a tree of 16-pointer nodes internally that are indexed
+on each level by nibbles from the index key in the same manner as in a radix
+tree. To improve memory efficiency, shortcuts can be emplaced to skip over
+what would otherwise be a series of single-occupancy nodes. Further, nodes
+pack leaf object pointers into spare space in the node rather than making an
+extra branch until as such time an object needs to be added to a full node.
+
+
+==============
+THE PUBLIC API
+==============
+
+The public API can be found in <linux/assoc_array.h>. The associative array is
+rooted on the following structure:
+
+ struct assoc_array {
+ ...
+ };
+
+The code is selected by enabling CONFIG_ASSOCIATIVE_ARRAY.
+
+
+EDIT SCRIPT
+-----------
+
+The insertion and deletion functions produce an 'edit script' that can later be
+applied to effect the changes without risking ENOMEM. This retains the
+preallocated metadata blocks that will be installed in the internal tree and
+keeps track of the metadata blocks that will be removed from the tree when the
+script is applied.
+
+This is also used to keep track of dead blocks and dead objects after the
+script has been applied so that they can be freed later. The freeing is done
+after an RCU grace period has passed - thus allowing access functions to
+proceed under the RCU read lock.
+
+The script appears as outside of the API as a pointer of the type:
+
+ struct assoc_array_edit;
+
+There are two functions for dealing with the script:
+
+ (1) Apply an edit script.
+
+ void assoc_array_apply_edit(struct assoc_array_edit *edit);
+
+ This will perform the edit functions, interpolating various write barriers
+ to permit accesses under the RCU read lock to continue. The edit script
+ will then be passed to call_rcu() to free it and any dead stuff it points
+ to.
+
+ (2) Cancel an edit script.
+
+ void assoc_array_cancel_edit(struct assoc_array_edit *edit);
+
+ This frees the edit script and all preallocated memory immediately. If
+ this was for insertion, the new object is _not_ released by this function,
+ but must rather be released by the caller.
+
+These functions are guaranteed not to fail.
+
+
+OPERATIONS TABLE
+----------------
+
+Various functions take a table of operations:
+
+ struct assoc_array_ops {
+ ...
+ };
+
+This points to a number of methods, all of which need to be provided:
+
+ (1) Get a chunk of index key from caller data:
+
+ unsigned long (*get_key_chunk)(const void *index_key, int level);
+
+ This should return a chunk of caller-supplied index key starting at the
+ *bit* position given by the level argument. The level argument will be a
+ multiple of ASSOC_ARRAY_KEY_CHUNK_SIZE and the function should return
+ ASSOC_ARRAY_KEY_CHUNK_SIZE bits. No error is possible.
+
+
+ (2) Get a chunk of an object's index key.
+
+ unsigned long (*get_object_key_chunk)(const void *object, int level);
+
+ As the previous function, but gets its data from an object in the array
+ rather than from a caller-supplied index key.
+
+
+ (3) See if this is the object we're looking for.
+
+ bool (*compare_object)(const void *object, const void *index_key);
+
+ Compare the object against an index key and return true if it matches and
+ false if it doesn't.
+
+
+ (4) Diff the index keys of two objects.
+
+ int (*diff_objects)(const void *object, const void *index_key);
+
+ Return the bit position at which the index key of the specified object
+ differs from the given index key or -1 if they are the same.
+
+
+ (5) Free an object.
+
+ void (*free_object)(void *object);
+
+ Free the specified object. Note that this may be called an RCU grace
+ period after assoc_array_apply_edit() was called, so synchronize_rcu() may
+ be necessary on module unloading.
+
+
+MANIPULATION FUNCTIONS
+----------------------
+
+There are a number of functions for manipulating an associative array:
+
+ (1) Initialise an associative array.
+
+ void assoc_array_init(struct assoc_array *array);
+
+ This initialises the base structure for an associative array. It can't
+ fail.
+
+
+ (2) Insert/replace an object in an associative array.
+
+ struct assoc_array_edit *
+ assoc_array_insert(struct assoc_array *array,
+ const struct assoc_array_ops *ops,
+ const void *index_key,
+ void *object);
+
+ This inserts the given object into the array. Note that the least
+ significant bit of the pointer must be zero as it's used to type-mark
+ pointers internally.
+
+ If an object already exists for that key then it will be replaced with the
+ new object and the old one will be freed automatically.
+
+ The index_key argument should hold index key information and is
+ passed to the methods in the ops table when they are called.
+
+ This function makes no alteration to the array itself, but rather returns
+ an edit script that must be applied. -ENOMEM is returned in the case of
+ an out-of-memory error.
+
+ The caller should lock exclusively against other modifiers of the array.
+
+
+ (3) Delete an object from an associative array.
+
+ struct assoc_array_edit *
+ assoc_array_delete(struct assoc_array *array,
+ const struct assoc_array_ops *ops,
+ const void *index_key);
+
+ This deletes an object that matches the specified data from the array.
+
+ The index_key argument should hold index key information and is
+ passed to the methods in the ops table when they are called.
+
+ This function makes no alteration to the array itself, but rather returns
+ an edit script that must be applied. -ENOMEM is returned in the case of
+ an out-of-memory error. NULL will be returned if the specified object is
+ not found within the array.
+
+ The caller should lock exclusively against other modifiers of the array.
+
+
+ (4) Delete all objects from an associative array.
+
+ struct assoc_array_edit *
+ assoc_array_clear(struct assoc_array *array,
+ const struct assoc_array_ops *ops);
+
+ This deletes all the objects from an associative array and leaves it
+ completely empty.
+
+ This function makes no alteration to the array itself, but rather returns
+ an edit script that must be applied. -ENOMEM is returned in the case of
+ an out-of-memory error.
+
+ The caller should lock exclusively against other modifiers of the array.
+
+
+ (5) Destroy an associative array, deleting all objects.
+
+ void assoc_array_destroy(struct assoc_array *array,
+ const struct assoc_array_ops *ops);
+
+ This destroys the contents of the associative array and leaves it
+ completely empty. It is not permitted for another thread to be traversing
+ the array under the RCU read lock at the same time as this function is
+ destroying it as no RCU deferral is performed on memory release -
+ something that would require memory to be allocated.
+
+ The caller should lock exclusively against other modifiers and accessors
+ of the array.
+
+
+ (6) Garbage collect an associative array.
+
+ int assoc_array_gc(struct assoc_array *array,
+ const struct assoc_array_ops *ops,
+ bool (*iterator)(void *object, void *iterator_data),
+ void *iterator_data);
+
+ This iterates over the objects in an associative array and passes each one
+ to iterator(). If iterator() returns true, the object is kept. If it
+ returns false, the object will be freed. If the iterator() function
+ returns true, it must perform any appropriate refcount incrementing on the
+ object before returning.
+
+ The internal tree will be packed down if possible as part of the iteration
+ to reduce the number of nodes in it.
+
+ The iterator_data is passed directly to iterator() and is otherwise
+ ignored by the function.
+
+ The function will return 0 if successful and -ENOMEM if there wasn't
+ enough memory.
+
+ It is possible for other threads to iterate over or search the array under
+ the RCU read lock whilst this function is in progress. The caller should
+ lock exclusively against other modifiers of the array.
+
+
+ACCESS FUNCTIONS
+----------------
+
+There are two functions for accessing an associative array:
+
+ (1) Iterate over all the objects in an associative array.
+
+ int assoc_array_iterate(const struct assoc_array *array,
+ int (*iterator)(const void *object,
+ void *iterator_data),
+ void *iterator_data);
+
+ This passes each object in the array to the iterator callback function.
+ iterator_data is private data for that function.
+
+ This may be used on an array at the same time as the array is being
+ modified, provided the RCU read lock is held. Under such circumstances,
+ it is possible for the iteration function to see some objects twice. If
+ this is a problem, then modification should be locked against. The
+ iteration algorithm should not, however, miss any objects.
+
+ The function will return 0 if no objects were in the array or else it will
+ return the result of the last iterator function called. Iteration stops
+ immediately if any call to the iteration function results in a non-zero
+ return.
+
+
+ (2) Find an object in an associative array.
+
+ void *assoc_array_find(const struct assoc_array *array,
+ const struct assoc_array_ops *ops,
+ const void *index_key);
+
+ This walks through the array's internal tree directly to the object
+ specified by the index key..
+
+ This may be used on an array at the same time as the array is being
+ modified, provided the RCU read lock is held.
+
+ The function will return the object if found (and set *_type to the object
+ type) or will return NULL if the object was not found.
+
+
+INDEX KEY FORM
+--------------
+
+The index key can be of any form, but since the algorithms aren't told how long
+the key is, it is strongly recommended that the index key includes its length
+very early on before any variation due to the length would have an effect on
+comparisons.
+
+This will cause leaves with different length keys to scatter away from each
+other - and those with the same length keys to cluster together.
+
+It is also recommended that the index key begin with a hash of the rest of the
+key to maximise scattering throughout keyspace.
+
+The better the scattering, the wider and lower the internal tree will be.
+
+Poor scattering isn't too much of a problem as there are shortcuts and nodes
+can contain mixtures of leaves and metadata pointers.
+
+The index key is read in chunks of machine word. Each chunk is subdivided into
+one nibble (4 bits) per level, so on a 32-bit CPU this is good for 8 levels and
+on a 64-bit CPU, 16 levels. Unless the scattering is really poor, it is
+unlikely that more than one word of any particular index key will have to be
+used.
+
+
+=================
+INTERNAL WORKINGS
+=================
+
+The associative array data structure has an internal tree. This tree is
+constructed of two types of metadata blocks: nodes and shortcuts.
+
+A node is an array of slots. Each slot can contain one of four things:
+
+ (*) A NULL pointer, indicating that the slot is empty.
+
+ (*) A pointer to an object (a leaf).
+
+ (*) A pointer to a node at the next level.
+
+ (*) A pointer to a shortcut.
+
+
+BASIC INTERNAL TREE LAYOUT
+--------------------------
+
+Ignoring shortcuts for the moment, the nodes form a multilevel tree. The index
+key space is strictly subdivided by the nodes in the tree and nodes occur on
+fixed levels. For example:
+
+ Level: 0 1 2 3
+ =============== =============== =============== ===============
+ NODE D
+ NODE B NODE C +------>+---+
+ +------>+---+ +------>+---+ | | 0 |
+ NODE A | | 0 | | | 0 | | +---+
+ +---+ | +---+ | +---+ | : :
+ | 0 | | : : | : : | +---+
+ +---+ | +---+ | +---+ | | f |
+ | 1 |---+ | 3 |---+ | 7 |---+ +---+
+ +---+ +---+ +---+
+ : : : : | 8 |---+
+ +---+ +---+ +---+ | NODE E
+ | e |---+ | f | : : +------>+---+
+ +---+ | +---+ +---+ | 0 |
+ | f | | | f | +---+
+ +---+ | +---+ : :
+ | NODE F +---+
+ +------>+---+ | f |
+ | 0 | NODE G +---+
+ +---+ +------>+---+
+ : : | | 0 |
+ +---+ | +---+
+ | 6 |---+ : :
+ +---+ +---+
+ : : | f |
+ +---+ +---+
+ | f |
+ +---+
+
+In the above example, there are 7 nodes (A-G), each with 16 slots (0-f).
+Assuming no other meta data nodes in the tree, the key space is divided thusly:
+
+ KEY PREFIX NODE
+ ========== ====
+ 137* D
+ 138* E
+ 13[0-69-f]* C
+ 1[0-24-f]* B
+ e6* G
+ e[0-57-f]* F
+ [02-df]* A
+
+So, for instance, keys with the following example index keys will be found in
+the appropriate nodes:
+
+ INDEX KEY PREFIX NODE
+ =============== ======= ====
+ 13694892892489 13 C
+ 13795289025897 137 D
+ 13889dde88793 138 E
+ 138bbb89003093 138 E
+ 1394879524789 12 C
+ 1458952489 1 B
+ 9431809de993ba - A
+ b4542910809cd - A
+ e5284310def98 e F
+ e68428974237 e6 G
+ e7fffcbd443 e F
+ f3842239082 - A
+
+To save memory, if a node can hold all the leaves in its portion of keyspace,
+then the node will have all those leaves in it and will not have any metadata
+pointers - even if some of those leaves would like to be in the same slot.
+
+A node can contain a heterogeneous mix of leaves and metadata pointers.
+Metadata pointers must be in the slots that match their subdivisions of key
+space. The leaves can be in any slot not occupied by a metadata pointer. It
+is guaranteed that none of the leaves in a node will match a slot occupied by a
+metadata pointer. If the metadata pointer is there, any leaf whose key matches
+the metadata key prefix must be in the subtree that the metadata pointer points
+to.
+
+In the above example list of index keys, node A will contain:
+
+ SLOT CONTENT INDEX KEY (PREFIX)
+ ==== =============== ==================
+ 1 PTR TO NODE B 1*
+ any LEAF 9431809de993ba
+ any LEAF b4542910809cd
+ e PTR TO NODE F e*
+ any LEAF f3842239082
+
+and node B:
+
+ 3 PTR TO NODE C 13*
+ any LEAF 1458952489
+
+
+SHORTCUTS
+---------
+
+Shortcuts are metadata records that jump over a piece of keyspace. A shortcut
+is a replacement for a series of single-occupancy nodes ascending through the
+levels. Shortcuts exist to save memory and to speed up traversal.
+
+It is possible for the root of the tree to be a shortcut - say, for example,
+the tree contains at least 17 nodes all with key prefix '1111'. The insertion
+algorithm will insert a shortcut to skip over the '1111' keyspace in a single
+bound and get to the fourth level where these actually become different.
+
+
+SPLITTING AND COLLAPSING NODES
+------------------------------
+
+Each node has a maximum capacity of 16 leaves and metadata pointers. If the
+insertion algorithm finds that it is trying to insert a 17th object into a
+node, that node will be split such that at least two leaves that have a common
+key segment at that level end up in a separate node rooted on that slot for
+that common key segment.
+
+If the leaves in a full node and the leaf that is being inserted are
+sufficiently similar, then a shortcut will be inserted into the tree.
+
+When the number of objects in the subtree rooted at a node falls to 16 or
+fewer, then the subtree will be collapsed down to a single node - and this will
+ripple towards the root if possible.
+
+
+NON-RECURSIVE ITERATION
+-----------------------
+
+Each node and shortcut contains a back pointer to its parent and the number of
+slot in that parent that points to it. None-recursive iteration uses these to
+proceed rootwards through the tree, going to the parent node, slot N + 1 to
+make sure progress is made without the need for a stack.
+
+The backpointers, however, make simultaneous alteration and iteration tricky.
+
+
+SIMULTANEOUS ALTERATION AND ITERATION
+-------------------------------------
+
+There are a number of cases to consider:
+
+ (1) Simple insert/replace. This involves simply replacing a NULL or old
+ matching leaf pointer with the pointer to the new leaf after a barrier.
+ The metadata blocks don't change otherwise. An old leaf won't be freed
+ until after the RCU grace period.
+
+ (2) Simple delete. This involves just clearing an old matching leaf. The
+ metadata blocks don't change otherwise. The old leaf won't be freed until
+ after the RCU grace period.
+
+ (3) Insertion replacing part of a subtree that we haven't yet entered. This
+ may involve replacement of part of that subtree - but that won't affect
+ the iteration as we won't have reached the pointer to it yet and the
+ ancestry blocks are not replaced (the layout of those does not change).
+
+ (4) Insertion replacing nodes that we're actively processing. This isn't a
+ problem as we've passed the anchoring pointer and won't switch onto the
+ new layout until we follow the back pointers - at which point we've
+ already examined the leaves in the replaced node (we iterate over all the
+ leaves in a node before following any of its metadata pointers).
+
+ We might, however, re-see some leaves that have been split out into a new
+ branch that's in a slot further along than we were at.
+
+ (5) Insertion replacing nodes that we're processing a dependent branch of.
+ This won't affect us until we follow the back pointers. Similar to (4).
+
+ (6) Deletion collapsing a branch under us. This doesn't affect us because the
+ back pointers will get us back to the parent of the new node before we
+ could see the new node. The entire collapsed subtree is thrown away
+ unchanged - and will still be rooted on the same slot, so we shouldn't
+ process it a second time as we'll go back to slot + 1.
+
+Note:
+
+ (*) Under some circumstances, we need to simultaneously change the parent
+ pointer and the parent slot pointer on a node (say, for example, we
+ inserted another node before it and moved it up a level). We cannot do
+ this without locking against a read - so we have to replace that node too.
+
+ However, when we're changing a shortcut into a node this isn't a problem
+ as shortcuts only have one slot and so the parent slot number isn't used
+ when traversing backwards over one. This means that it's okay to change
+ the slot number first - provided suitable barriers are used to make sure
+ the parent slot number is read after the back pointer.
+
+Obsolete blocks and leaves are freed up after an RCU grace period has passed,
+so as long as anyone doing walking or iteration holds the RCU read lock, the
+old superstructure should not go away on them.