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