| ======================================== | |
| Generic Associative Array Implementation | |
| ======================================== | |
| 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`` with:: | |
| ./script/config -e 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. |