1========================================
2Generic Associative Array Implementation
3========================================
4
5Overview
6========
7
8This associative array implementation is an object container with the following
9properties:
10
111. Objects are opaque pointers.  The implementation does not care where they
12   point (if anywhere) or what they point to (if anything).
13.. note:: Pointers to objects _must_ be zero in the least significant bit.
14
152. Objects do not need to contain linkage blocks for use by the array.  This
16   permits an object to be located in multiple arrays simultaneously.
17   Rather, the array is made up of metadata blocks that point to objects.
18
193. Objects require index keys to locate them within the array.
20
214. Index keys must be unique.  Inserting an object with the same key as one
22   already in the array will replace the old object.
23
245. Index keys can be of any length and can be of different lengths.
25
266. Index keys should encode the length early on, before any variation due to
27   length is seen.
28
297. Index keys can include a hash to scatter objects throughout the array.
30
318. The array can iterated over.  The objects will not necessarily come out in
32   key order.
33
349. The array can be iterated over whilst it is being modified, provided the
35   RCU readlock is being held by the iterator.  Note, however, under these
36   circumstances, some objects may be seen more than once.  If this is a
37   problem, the iterator should lock against modification.  Objects will not
38   be missed, however, unless deleted.
39
4010. Objects in the array can be looked up by means of their index key.
41
4211. Objects can be looked up whilst the array is being modified, provided the
43    RCU readlock is being held by the thread doing the look up.
44
45The implementation uses a tree of 16-pointer nodes internally that are indexed
46on each level by nibbles from the index key in the same manner as in a radix
47tree.  To improve memory efficiency, shortcuts can be emplaced to skip over
48what would otherwise be a series of single-occupancy nodes.  Further, nodes
49pack leaf object pointers into spare space in the node rather than making an
50extra branch until as such time an object needs to be added to a full node.
51
52
53The Public API
54==============
55
56The public API can be found in ``<linux/assoc_array.h>``.  The associative
57array is rooted on the following structure::
58
59    struct assoc_array {
60            ...
61    };
62
63The code is selected by enabling ``CONFIG_ASSOCIATIVE_ARRAY`` with::
64
65    ./script/config -e ASSOCIATIVE_ARRAY
66
67
68Edit Script
69-----------
70
71The insertion and deletion functions produce an 'edit script' that can later be
72applied to effect the changes without risking ``ENOMEM``. This retains the
73preallocated metadata blocks that will be installed in the internal tree and
74keeps track of the metadata blocks that will be removed from the tree when the
75script is applied.
76
77This is also used to keep track of dead blocks and dead objects after the
78script has been applied so that they can be freed later.  The freeing is done
79after an RCU grace period has passed - thus allowing access functions to
80proceed under the RCU read lock.
81
82The script appears as outside of the API as a pointer of the type::
83
84    struct assoc_array_edit;
85
86There are two functions for dealing with the script:
87
881. Apply an edit script::
89
90    void assoc_array_apply_edit(struct assoc_array_edit *edit);
91
92This will perform the edit functions, interpolating various write barriers
93to permit accesses under the RCU read lock to continue.  The edit script
94will then be passed to ``call_rcu()`` to free it and any dead stuff it points
95to.
96
972. Cancel an edit script::
98
99    void assoc_array_cancel_edit(struct assoc_array_edit *edit);
100
101This frees the edit script and all preallocated memory immediately. If
102this was for insertion, the new object is _not_ released by this function,
103but must rather be released by the caller.
104
105These functions are guaranteed not to fail.
106
107
108Operations Table
109----------------
110
111Various functions take a table of operations::
112
113    struct assoc_array_ops {
114            ...
115    };
116
117This points to a number of methods, all of which need to be provided:
118
1191. Get a chunk of index key from caller data::
120
121    unsigned long (*get_key_chunk)(const void *index_key, int level);
122
123This should return a chunk of caller-supplied index key starting at the
124*bit* position given by the level argument.  The level argument will be a
125multiple of ``ASSOC_ARRAY_KEY_CHUNK_SIZE`` and the function should return
126``ASSOC_ARRAY_KEY_CHUNK_SIZE bits``.  No error is possible.
127
128
1292. Get a chunk of an object's index key::
130
131    unsigned long (*get_object_key_chunk)(const void *object, int level);
132
133As the previous function, but gets its data from an object in the array
134rather than from a caller-supplied index key.
135
136
1373. See if this is the object we're looking for::
138
139    bool (*compare_object)(const void *object, const void *index_key);
140
141Compare the object against an index key and return ``true`` if it matches and
142``false`` if it doesn't.
143
144
1454. Diff the index keys of two objects::
146
147    int (*diff_objects)(const void *object, const void *index_key);
148
149Return the bit position at which the index key of the specified object
150differs from the given index key or -1 if they are the same.
151
152
1535. Free an object::
154
155    void (*free_object)(void *object);
156
157Free the specified object.  Note that this may be called an RCU grace period
158after ``assoc_array_apply_edit()`` was called, so ``synchronize_rcu()`` may be
159necessary on module unloading.
160
161
162Manipulation Functions
163----------------------
164
165There are a number of functions for manipulating an associative array:
166
1671. Initialise an associative array::
168
169    void assoc_array_init(struct assoc_array *array);
170
171This initialises the base structure for an associative array.  It can't fail.
172
173
1742. Insert/replace an object in an associative array::
175
176    struct assoc_array_edit *
177    assoc_array_insert(struct assoc_array *array,
178                       const struct assoc_array_ops *ops,
179                       const void *index_key,
180                       void *object);
181
182This inserts the given object into the array.  Note that the least
183significant bit of the pointer must be zero as it's used to type-mark
184pointers internally.
185
186If an object already exists for that key then it will be replaced with the
187new object and the old one will be freed automatically.
188
189The ``index_key`` argument should hold index key information and is
190passed to the methods in the ops table when they are called.
191
192This function makes no alteration to the array itself, but rather returns
193an edit script that must be applied.  ``-ENOMEM`` is returned in the case of
194an out-of-memory error.
195
196The caller should lock exclusively against other modifiers of the array.
197
198
1993. Delete an object from an associative array::
200
201    struct assoc_array_edit *
202    assoc_array_delete(struct assoc_array *array,
203                       const struct assoc_array_ops *ops,
204                       const void *index_key);
205
206This deletes an object that matches the specified data from the array.
207
208The ``index_key`` argument should hold index key information and is
209passed to the methods in the ops table when they are called.
210
211This function makes no alteration to the array itself, but rather returns
212an edit script that must be applied.  ``-ENOMEM`` is returned in the case of
213an out-of-memory error.  ``NULL`` will be returned if the specified object is
214not found within the array.
215
216The caller should lock exclusively against other modifiers of the array.
217
218
2194. Delete all objects from an associative array::
220
221    struct assoc_array_edit *
222    assoc_array_clear(struct assoc_array *array,
223                      const struct assoc_array_ops *ops);
224
225This deletes all the objects from an associative array and leaves it
226completely empty.
227
228This function makes no alteration to the array itself, but rather returns
229an edit script that must be applied.  ``-ENOMEM`` is returned in the case of
230an out-of-memory error.
231
232The caller should lock exclusively against other modifiers of the array.
233
234
2355. Destroy an associative array, deleting all objects::
236
237    void assoc_array_destroy(struct assoc_array *array,
238                             const struct assoc_array_ops *ops);
239
240This destroys the contents of the associative array and leaves it
241completely empty.  It is not permitted for another thread to be traversing
242the array under the RCU read lock at the same time as this function is
243destroying it as no RCU deferral is performed on memory release -
244something that would require memory to be allocated.
245
246The caller should lock exclusively against other modifiers and accessors
247of the array.
248
249
2506. Garbage collect an associative array::
251
252    int assoc_array_gc(struct assoc_array *array,
253                       const struct assoc_array_ops *ops,
254                       bool (*iterator)(void *object, void *iterator_data),
255                       void *iterator_data);
256
257This iterates over the objects in an associative array and passes each one to
258``iterator()``.  If ``iterator()`` returns ``true``, the object is kept.  If it
259returns ``false``, the object will be freed.  If the ``iterator()`` function
260returns ``true``, it must perform any appropriate refcount incrementing on the
261object before returning.
262
263The internal tree will be packed down if possible as part of the iteration
264to reduce the number of nodes in it.
265
266The ``iterator_data`` is passed directly to ``iterator()`` and is otherwise
267ignored by the function.
268
269The function will return ``0`` if successful and ``-ENOMEM`` if there wasn't
270enough memory.
271
272It is possible for other threads to iterate over or search the array under
273the RCU read lock whilst this function is in progress.  The caller should
274lock exclusively against other modifiers of the array.
275
276
277Access Functions
278----------------
279
280There are two functions for accessing an associative array:
281
2821. Iterate over all the objects in an associative array::
283
284    int assoc_array_iterate(const struct assoc_array *array,
285                            int (*iterator)(const void *object,
286                                            void *iterator_data),
287                            void *iterator_data);
288
289This passes each object in the array to the iterator callback function.
290``iterator_data`` is private data for that function.
291
292This may be used on an array at the same time as the array is being
293modified, provided the RCU read lock is held.  Under such circumstances,
294it is possible for the iteration function to see some objects twice.  If
295this is a problem, then modification should be locked against.  The
296iteration algorithm should not, however, miss any objects.
297
298The function will return ``0`` if no objects were in the array or else it will
299return the result of the last iterator function called.  Iteration stops
300immediately if any call to the iteration function results in a non-zero
301return.
302
303
3042. Find an object in an associative array::
305
306    void *assoc_array_find(const struct assoc_array *array,
307                           const struct assoc_array_ops *ops,
308                           const void *index_key);
309
310This walks through the array's internal tree directly to the object
311specified by the index key..
312
313This may be used on an array at the same time as the array is being
314modified, provided the RCU read lock is held.
315
316The function will return the object if found (and set ``*_type`` to the object
317type) or will return ``NULL`` if the object was not found.
318
319
320Index Key Form
321--------------
322
323The index key can be of any form, but since the algorithms aren't told how long
324the key is, it is strongly recommended that the index key includes its length
325very early on before any variation due to the length would have an effect on
326comparisons.
327
328This will cause leaves with different length keys to scatter away from each
329other - and those with the same length keys to cluster together.
330
331It is also recommended that the index key begin with a hash of the rest of the
332key to maximise scattering throughout keyspace.
333
334The better the scattering, the wider and lower the internal tree will be.
335
336Poor scattering isn't too much of a problem as there are shortcuts and nodes
337can contain mixtures of leaves and metadata pointers.
338
339The index key is read in chunks of machine word.  Each chunk is subdivided into
340one nibble (4 bits) per level, so on a 32-bit CPU this is good for 8 levels and
341on a 64-bit CPU, 16 levels.  Unless the scattering is really poor, it is
342unlikely that more than one word of any particular index key will have to be
343used.
344
345
346Internal Workings
347=================
348
349The associative array data structure has an internal tree.  This tree is
350constructed of two types of metadata blocks: nodes and shortcuts.
351
352A node is an array of slots.  Each slot can contain one of four things:
353
354* A NULL pointer, indicating that the slot is empty.
355* A pointer to an object (a leaf).
356* A pointer to a node at the next level.
357* A pointer to a shortcut.
358
359
360Basic Internal Tree Layout
361--------------------------
362
363Ignoring shortcuts for the moment, the nodes form a multilevel tree.  The index
364key space is strictly subdivided by the nodes in the tree and nodes occur on
365fixed levels.  For example::
366
367 Level: 0               1               2               3
368        =============== =============== =============== ===============
369                                                        NODE D
370                        NODE B          NODE C  +------>+---+
371                +------>+---+   +------>+---+   |       | 0 |
372        NODE A  |       | 0 |   |       | 0 |   |       +---+
373        +---+   |       +---+   |       +---+   |       :   :
374        | 0 |   |       :   :   |       :   :   |       +---+
375        +---+   |       +---+   |       +---+   |       | f |
376        | 1 |---+       | 3 |---+       | 7 |---+       +---+
377        +---+           +---+           +---+
378        :   :           :   :           | 8 |---+
379        +---+           +---+           +---+   |       NODE E
380        | e |---+       | f |           :   :   +------>+---+
381        +---+   |       +---+           +---+           | 0 |
382        | f |   |                       | f |           +---+
383        +---+   |                       +---+           :   :
384                |       NODE F                          +---+
385                +------>+---+                           | f |
386                        | 0 |           NODE G          +---+
387                        +---+   +------>+---+
388                        :   :   |       | 0 |
389                        +---+   |       +---+
390                        | 6 |---+       :   :
391                        +---+           +---+
392                        :   :           | f |
393                        +---+           +---+
394                        | f |
395                        +---+
396
397In the above example, there are 7 nodes (A-G), each with 16 slots (0-f).
398Assuming no other meta data nodes in the tree, the key space is divided
399thusly::
400
401    KEY PREFIX      NODE
402    ==========      ====
403    137*            D
404    138*            E
405    13[0-69-f]*     C
406    1[0-24-f]*      B
407    e6*             G
408    e[0-57-f]*      F
409    [02-df]*        A
410
411So, for instance, keys with the following example index keys will be found in
412the appropriate nodes::
413
414    INDEX KEY       PREFIX  NODE
415    =============== ======= ====
416    13694892892489  13      C
417    13795289025897  137     D
418    13889dde88793   138     E
419    138bbb89003093  138     E
420    1394879524789   12      C
421    1458952489      1       B
422    9431809de993ba  -       A
423    b4542910809cd   -       A
424    e5284310def98   e       F
425    e68428974237    e6      G
426    e7fffcbd443     e       F
427    f3842239082     -       A
428
429To save memory, if a node can hold all the leaves in its portion of keyspace,
430then the node will have all those leaves in it and will not have any metadata
431pointers - even if some of those leaves would like to be in the same slot.
432
433A node can contain a heterogeneous mix of leaves and metadata pointers.
434Metadata pointers must be in the slots that match their subdivisions of key
435space.  The leaves can be in any slot not occupied by a metadata pointer.  It
436is guaranteed that none of the leaves in a node will match a slot occupied by a
437metadata pointer.  If the metadata pointer is there, any leaf whose key matches
438the metadata key prefix must be in the subtree that the metadata pointer points
439to.
440
441In the above example list of index keys, node A will contain::
442
443    SLOT    CONTENT         INDEX KEY (PREFIX)
444    ====    =============== ==================
445    1       PTR TO NODE B   1*
446    any     LEAF            9431809de993ba
447    any     LEAF            b4542910809cd
448    e       PTR TO NODE F   e*
449    any     LEAF            f3842239082
450
451and node B::
452
453    3	PTR TO NODE C	13*
454    any	LEAF		1458952489
455
456
457Shortcuts
458---------
459
460Shortcuts are metadata records that jump over a piece of keyspace.  A shortcut
461is a replacement for a series of single-occupancy nodes ascending through the
462levels.  Shortcuts exist to save memory and to speed up traversal.
463
464It is possible for the root of the tree to be a shortcut - say, for example,
465the tree contains at least 17 nodes all with key prefix ``1111``.  The
466insertion algorithm will insert a shortcut to skip over the ``1111`` keyspace
467in a single bound and get to the fourth level where these actually become
468different.
469
470
471Splitting And Collapsing Nodes
472------------------------------
473
474Each node has a maximum capacity of 16 leaves and metadata pointers.  If the
475insertion algorithm finds that it is trying to insert a 17th object into a
476node, that node will be split such that at least two leaves that have a common
477key segment at that level end up in a separate node rooted on that slot for
478that common key segment.
479
480If the leaves in a full node and the leaf that is being inserted are
481sufficiently similar, then a shortcut will be inserted into the tree.
482
483When the number of objects in the subtree rooted at a node falls to 16 or
484fewer, then the subtree will be collapsed down to a single node - and this will
485ripple towards the root if possible.
486
487
488Non-Recursive Iteration
489-----------------------
490
491Each node and shortcut contains a back pointer to its parent and the number of
492slot in that parent that points to it.  None-recursive iteration uses these to
493proceed rootwards through the tree, going to the parent node, slot N + 1 to
494make sure progress is made without the need for a stack.
495
496The backpointers, however, make simultaneous alteration and iteration tricky.
497
498
499Simultaneous Alteration And Iteration
500-------------------------------------
501
502There are a number of cases to consider:
503
5041. Simple insert/replace.  This involves simply replacing a NULL or old
505   matching leaf pointer with the pointer to the new leaf after a barrier.
506   The metadata blocks don't change otherwise.  An old leaf won't be freed
507   until after the RCU grace period.
508
5092. Simple delete.  This involves just clearing an old matching leaf.  The
510   metadata blocks don't change otherwise.  The old leaf won't be freed until
511   after the RCU grace period.
512
5133. Insertion replacing part of a subtree that we haven't yet entered.  This
514   may involve replacement of part of that subtree - but that won't affect
515   the iteration as we won't have reached the pointer to it yet and the
516   ancestry blocks are not replaced (the layout of those does not change).
517
5184. Insertion replacing nodes that we're actively processing.  This isn't a
519   problem as we've passed the anchoring pointer and won't switch onto the
520   new layout until we follow the back pointers - at which point we've
521   already examined the leaves in the replaced node (we iterate over all the
522   leaves in a node before following any of its metadata pointers).
523
524   We might, however, re-see some leaves that have been split out into a new
525   branch that's in a slot further along than we were at.
526
5275. Insertion replacing nodes that we're processing a dependent branch of.
528   This won't affect us until we follow the back pointers.  Similar to (4).
529
5306. Deletion collapsing a branch under us.  This doesn't affect us because the
531   back pointers will get us back to the parent of the new node before we
532   could see the new node.  The entire collapsed subtree is thrown away
533   unchanged - and will still be rooted on the same slot, so we shouldn't
534   process it a second time as we'll go back to slot + 1.
535
536.. note::
537
538   Under some circumstances, we need to simultaneously change the parent
539   pointer and the parent slot pointer on a node (say, for example, we
540   inserted another node before it and moved it up a level).  We cannot do
541   this without locking against a read - so we have to replace that node too.
542
543   However, when we're changing a shortcut into a node this isn't a problem
544   as shortcuts only have one slot and so the parent slot number isn't used
545   when traversing backwards over one.  This means that it's okay to change
546   the slot number first - provided suitable barriers are used to make sure
547   the parent slot number is read after the back pointer.
548
549Obsolete blocks and leaves are freed up after an RCU grace period has passed,
550so as long as anyone doing walking or iteration holds the RCU read lock, the
551old superstructure should not go away on them.
552