1 ========================================
2 Generic Associative Array Implementation
3 ========================================
4
5 Overview
6 ========
7
8 This associative array implementation is an object container with the following
9 properties:
10
11 1. Objects are opaque pointers. The implementation does not care where they
12 point (if anywhere) or what they point to (if anything).
13
14 .. note::
15
16 Pointers to objects _must_ be zero in the least significant bit.
17
18 2. Objects do not need to contain linkage blocks for use by the array. This
19 permits an object to be located in multiple arrays simultaneously.
20 Rather, the array is made up of metadata blocks that point to objects.
21
22 3. Objects require index keys to locate them within the array.
23
24 4. Index keys must be unique. Inserting an object with the same key as one
25 already in the array will replace the old object.
26
27 5. Index keys can be of any length and can be of different lengths.
28
29 6. Index keys should encode the length early on, before any variation due to
30 length is seen.
31
32 7. Index keys can include a hash to scatter objects throughout the array.
33
34 8. The array can iterated over. The objects will not necessarily come out in
35 key order.
36
37 9. The array can be iterated over while it is being modified, provided the
38 RCU readlock is being held by the iterator. Note, however, under these
39 circumstances, some objects may be seen more than once. If this is a
40 problem, the iterator should lock against modification. Objects will not
41 be missed, however, unless deleted.
42
43 10. Objects in the array can be looked up by means of their index key.
44
45 11. Objects can be looked up while the array is being modified, provided the
46 RCU readlock is being held by the thread doing the look up.
47
48 The implementation uses a tree of 16-pointer nodes internally that are indexed
49 on each level by nibbles from the index key in the same manner as in a radix
50 tree. To improve memory efficiency, shortcuts can be emplaced to skip over
51 what would otherwise be a series of single-occupancy nodes. Further, nodes
52 pack leaf object pointers into spare space in the node rather than making an
53 extra branch until as such time an object needs to be added to a full node.
54
55
56 The Public API
57 ==============
58
59 The public API can be found in ``<linux/assoc_array.h>``. The associative
60 array is rooted on the following structure::
61
62 struct assoc_array {
63 ...
64 };
65
66 The code is selected by enabling ``CONFIG_ASSOCIATIVE_ARRAY`` with::
67
68 ./script/config -e ASSOCIATIVE_ARRAY
69
70
71 Edit Script
72 -----------
73
74 The insertion and deletion functions produce an 'edit script' that can later be
75 applied to effect the changes without risking ``ENOMEM``. This retains the
76 preallocated metadata blocks that will be installed in the internal tree and
77 keeps track of the metadata blocks that will be removed from the tree when the
78 script is applied.
79
80 This is also used to keep track of dead blocks and dead objects after the
81 script has been applied so that they can be freed later. The freeing is done
82 after an RCU grace period has passed - thus allowing access functions to
83 proceed under the RCU read lock.
84
85 The script appears as outside of the API as a pointer of the type::
86
87 struct assoc_array_edit;
88
89 There are two functions for dealing with the script:
90
91 1. Apply an edit script::
92
93 void assoc_array_apply_edit(struct assoc_array_edit *edit);
94
95 This will perform the edit functions, interpolating various write barriers
96 to permit accesses under the RCU read lock to continue. The edit script
97 will then be passed to ``call_rcu()`` to free it and any dead stuff it points
98 to.
99
100 2. Cancel an edit script::
101
102 void assoc_array_cancel_edit(struct assoc_array_edit *edit);
103
104 This frees the edit script and all preallocated memory immediately. If
105 this was for insertion, the new object is _not_ released by this function,
106 but must rather be released by the caller.
107
108 These functions are guaranteed not to fail.
109
110
111 Operations Table
112 ----------------
113
114 Various functions take a table of operations::
115
116 struct assoc_array_ops {
117 ...
118 };
119
120 This points to a number of methods, all of which need to be provided:
121
122 1. Get a chunk of index key from caller data::
123
124 unsigned long (*get_key_chunk)(const void *index_key, int level);
125
126 This should return a chunk of caller-supplied index key starting at the
127 *bit* position given by the level argument. The level argument will be a
128 multiple of ``ASSOC_ARRAY_KEY_CHUNK_SIZE`` and the function should return
129 ``ASSOC_ARRAY_KEY_CHUNK_SIZE bits``. No error is possible.
130
131
132 2. Get a chunk of an object's index key::
133
134 unsigned long (*get_object_key_chunk)(const void *object, int level);
135
136 As the previous function, but gets its data from an object in the array
137 rather than from a caller-supplied index key.
138
139
140 3. See if this is the object we're looking for::
141
142 bool (*compare_object)(const void *object, const void *index_key);
143
144 Compare the object against an index key and return ``true`` if it matches and
145 ``false`` if it doesn't.
146
147
148 4. Diff the index keys of two objects::
149
150 int (*diff_objects)(const void *object, const void *index_key);
151
152 Return the bit position at which the index key of the specified object
153 differs from the given index key or -1 if they are the same.
154
155
156 5. Free an object::
157
158 void (*free_object)(void *object);
159
160 Free the specified object. Note that this may be called an RCU grace period
161 after ``assoc_array_apply_edit()`` was called, so ``synchronize_rcu()`` may be
162 necessary on module unloading.
163
164
165 Manipulation Functions
166 ----------------------
167
168 There are a number of functions for manipulating an associative array:
169
170 1. Initialise an associative array::
171
172 void assoc_array_init(struct assoc_array *array);
173
174 This initialises the base structure for an associative array. It can't fail.
175
176
177 2. Insert/replace an object in an associative array::
178
179 struct assoc_array_edit *
180 assoc_array_insert(struct assoc_array *array,
181 const struct assoc_array_ops *ops,
182 const void *index_key,
183 void *object);
184
185 This inserts the given object into the array. Note that the least
186 significant bit of the pointer must be zero as it's used to type-mark
187 pointers internally.
188
189 If an object already exists for that key then it will be replaced with the
190 new object and the old one will be freed automatically.
191
192 The ``index_key`` argument should hold index key information and is
193 passed to the methods in the ops table when they are called.
194
195 This function makes no alteration to the array itself, but rather returns
196 an edit script that must be applied. ``-ENOMEM`` is returned in the case of
197 an out-of-memory error.
198
199 The caller should lock exclusively against other modifiers of the array.
200
201
202 3. Delete an object from an associative array::
203
204 struct assoc_array_edit *
205 assoc_array_delete(struct assoc_array *array,
206 const struct assoc_array_ops *ops,
207 const void *index_key);
208
209 This deletes an object that matches the specified data from the array.
210
211 The ``index_key`` argument should hold index key information and is
212 passed to the methods in the ops table when they are called.
213
214 This function makes no alteration to the array itself, but rather returns
215 an edit script that must be applied. ``-ENOMEM`` is returned in the case of
216 an out-of-memory error. ``NULL`` will be returned if the specified object is
217 not found within the array.
218
219 The caller should lock exclusively against other modifiers of the array.
220
221
222 4. Delete all objects from an associative array::
223
224 struct assoc_array_edit *
225 assoc_array_clear(struct assoc_array *array,
226 const struct assoc_array_ops *ops);
227
228 This deletes all the objects from an associative array and leaves it
229 completely empty.
230
231 This function makes no alteration to the array itself, but rather returns
232 an edit script that must be applied. ``-ENOMEM`` is returned in the case of
233 an out-of-memory error.
234
235 The caller should lock exclusively against other modifiers of the array.
236
237
238 5. Destroy an associative array, deleting all objects::
239
240 void assoc_array_destroy(struct assoc_array *array,
241 const struct assoc_array_ops *ops);
242
243 This destroys the contents of the associative array and leaves it
244 completely empty. It is not permitted for another thread to be traversing
245 the array under the RCU read lock at the same time as this function is
246 destroying it as no RCU deferral is performed on memory release -
247 something that would require memory to be allocated.
248
249 The caller should lock exclusively against other modifiers and accessors
250 of the array.
251
252
253 6. Garbage collect an associative array::
254
255 int assoc_array_gc(struct assoc_array *array,
256 const struct assoc_array_ops *ops,
257 bool (*iterator)(void *object, void *iterator_data),
258 void *iterator_data);
259
260 This iterates over the objects in an associative array and passes each one to
261 ``iterator()``. If ``iterator()`` returns ``true``, the object is kept. If it
262 returns ``false``, the object will be freed. If the ``iterator()`` function
263 returns ``true``, it must perform any appropriate refcount incrementing on the
264 object before returning.
265
266 The internal tree will be packed down if possible as part of the iteration
267 to reduce the number of nodes in it.
268
269 The ``iterator_data`` is passed directly to ``iterator()`` and is otherwise
270 ignored by the function.
271
272 The function will return ``0`` if successful and ``-ENOMEM`` if there wasn't
273 enough memory.
274
275 It is possible for other threads to iterate over or search the array under
276 the RCU read lock while this function is in progress. The caller should
277 lock exclusively against other modifiers of the array.
278
279
280 Access Functions
281 ----------------
282
283 There are two functions for accessing an associative array:
284
285 1. Iterate over all the objects in an associative array::
286
287 int assoc_array_iterate(const struct assoc_array *array,
288 int (*iterator)(const void *object,
289 void *iterator_data),
290 void *iterator_data);
291
292 This passes each object in the array to the iterator callback function.
293 ``iterator_data`` is private data for that function.
294
295 This may be used on an array at the same time as the array is being
296 modified, provided the RCU read lock is held. Under such circumstances,
297 it is possible for the iteration function to see some objects twice. If
298 this is a problem, then modification should be locked against. The
299 iteration algorithm should not, however, miss any objects.
300
301 The function will return ``0`` if no objects were in the array or else it will
302 return the result of the last iterator function called. Iteration stops
303 immediately if any call to the iteration function results in a non-zero
304 return.
305
306
307 2. Find an object in an associative array::
308
309 void *assoc_array_find(const struct assoc_array *array,
310 const struct assoc_array_ops *ops,
311 const void *index_key);
312
313 This walks through the array's internal tree directly to the object
314 specified by the index key..
315
316 This may be used on an array at the same time as the array is being
317 modified, provided the RCU read lock is held.
318
319 The function will return the object if found (and set ``*_type`` to the object
320 type) or will return ``NULL`` if the object was not found.
321
322
323 Index Key Form
324 --------------
325
326 The index key can be of any form, but since the algorithms aren't told how long
327 the key is, it is strongly recommended that the index key includes its length
328 very early on before any variation due to the length would have an effect on
329 comparisons.
330
331 This will cause leaves with different length keys to scatter away from each
332 other - and those with the same length keys to cluster together.
333
334 It is also recommended that the index key begin with a hash of the rest of the
335 key to maximise scattering throughout keyspace.
336
337 The better the scattering, the wider and lower the internal tree will be.
338
339 Poor scattering isn't too much of a problem as there are shortcuts and nodes
340 can contain mixtures of leaves and metadata pointers.
341
342 The index key is read in chunks of machine word. Each chunk is subdivided into
343 one nibble (4 bits) per level, so on a 32-bit CPU this is good for 8 levels and
344 on a 64-bit CPU, 16 levels. Unless the scattering is really poor, it is
345 unlikely that more than one word of any particular index key will have to be
346 used.
347
348
349 Internal Workings
350 =================
351
352 The associative array data structure has an internal tree. This tree is
353 constructed of two types of metadata blocks: nodes and shortcuts.
354
355 A node is an array of slots. Each slot can contain one of four things:
356
357 * A NULL pointer, indicating that the slot is empty.
358 * A pointer to an object (a leaf).
359 * A pointer to a node at the next level.
360 * A pointer to a shortcut.
361
362
363 Basic Internal Tree Layout
364 --------------------------
365
366 Ignoring shortcuts for the moment, the nodes form a multilevel tree. The index
367 key space is strictly subdivided by the nodes in the tree and nodes occur on
368 fixed levels. For example::
369
370 Level: 0 1 2 3
371 =============== =============== =============== ===============
372 NODE D
373 NODE B NODE C +------>+---+
374 +------>+---+ +------>+---+ | | 0 |
375 NODE A | | 0 | | | 0 | | +---+
376 +---+ | +---+ | +---+ | : :
377 | 0 | | : : | : : | +---+
378 +---+ | +---+ | +---+ | | f |
379 | 1 |---+ | 3 |---+ | 7 |---+ +---+
380 +---+ +---+ +---+
381 : : : : | 8 |---+
382 +---+ +---+ +---+ | NODE E
383 | e |---+ | f | : : +------>+---+
384 +---+ | +---+ +---+ | 0 |
385 | f | | | f | +---+
386 +---+ | +---+ : :
387 | NODE F +---+
388 +------>+---+ | f |
389 | 0 | NODE G +---+
390 +---+ +------>+---+
391 : : | | 0 |
392 +---+ | +---+
393 | 6 |---+ : :
394 +---+ +---+
395 : : | f |
396 +---+ +---+
397 | f |
398 +---+
399
400 In the above example, there are 7 nodes (A-G), each with 16 slots (0-f).
401 Assuming no other meta data nodes in the tree, the key space is divided
402 thusly::
403
404 KEY PREFIX NODE
405 ========== ====
406 137* D
407 138* E
408 13[0-69-f]* C
409 1[0-24-f]* B
410 e6* G
411 e[0-57-f]* F
412 [02-df]* A
413
414 So, for instance, keys with the following example index keys will be found in
415 the appropriate nodes::
416
417 INDEX KEY PREFIX NODE
418 =============== ======= ====
419 13694892892489 13 C
420 13795289025897 137 D
421 13889dde88793 138 E
422 138bbb89003093 138 E
423 1394879524789 12 C
424 1458952489 1 B
425 9431809de993ba - A
426 b4542910809cd - A
427 e5284310def98 e F
428 e68428974237 e6 G
429 e7fffcbd443 e F
430 f3842239082 - A
431
432 To save memory, if a node can hold all the leaves in its portion of keyspace,
433 then the node will have all those leaves in it and will not have any metadata
434 pointers - even if some of those leaves would like to be in the same slot.
435
436 A node can contain a heterogeneous mix of leaves and metadata pointers.
437 Metadata pointers must be in the slots that match their subdivisions of key
438 space. The leaves can be in any slot not occupied by a metadata pointer. It
439 is guaranteed that none of the leaves in a node will match a slot occupied by a
440 metadata pointer. If the metadata pointer is there, any leaf whose key matches
441 the metadata key prefix must be in the subtree that the metadata pointer points
442 to.
443
444 In the above example list of index keys, node A will contain::
445
446 SLOT CONTENT INDEX KEY (PREFIX)
447 ==== =============== ==================
448 1 PTR TO NODE B 1*
449 any LEAF 9431809de993ba
450 any LEAF b4542910809cd
451 e PTR TO NODE F e*
452 any LEAF f3842239082
453
454 and node B::
455
456 3 PTR TO NODE C 13*
457 any LEAF 1458952489
458
459
460 Shortcuts
461 ---------
462
463 Shortcuts are metadata records that jump over a piece of keyspace. A shortcut
464 is a replacement for a series of single-occupancy nodes ascending through the
465 levels. Shortcuts exist to save memory and to speed up traversal.
466
467 It is possible for the root of the tree to be a shortcut - say, for example,
468 the tree contains at least 17 nodes all with key prefix ``1111``. The
469 insertion algorithm will insert a shortcut to skip over the ``1111`` keyspace
470 in a single bound and get to the fourth level where these actually become
471 different.
472
473
474 Splitting And Collapsing Nodes
475 ------------------------------
476
477 Each node has a maximum capacity of 16 leaves and metadata pointers. If the
478 insertion algorithm finds that it is trying to insert a 17th object into a
479 node, that node will be split such that at least two leaves that have a common
480 key segment at that level end up in a separate node rooted on that slot for
481 that common key segment.
482
483 If the leaves in a full node and the leaf that is being inserted are
484 sufficiently similar, then a shortcut will be inserted into the tree.
485
486 When the number of objects in the subtree rooted at a node falls to 16 or
487 fewer, then the subtree will be collapsed down to a single node - and this will
488 ripple towards the root if possible.
489
490
491 Non-Recursive Iteration
492 -----------------------
493
494 Each node and shortcut contains a back pointer to its parent and the number of
495 slot in that parent that points to it. None-recursive iteration uses these to
496 proceed rootwards through the tree, going to the parent node, slot N + 1 to
497 make sure progress is made without the need for a stack.
498
499 The backpointers, however, make simultaneous alteration and iteration tricky.
500
501
502 Simultaneous Alteration And Iteration
503 -------------------------------------
504
505 There are a number of cases to consider:
506
507 1. Simple insert/replace. This involves simply replacing a NULL or old
508 matching leaf pointer with the pointer to the new leaf after a barrier.
509 The metadata blocks don't change otherwise. An old leaf won't be freed
510 until after the RCU grace period.
511
512 2. Simple delete. This involves just clearing an old matching leaf. The
513 metadata blocks don't change otherwise. The old leaf won't be freed until
514 after the RCU grace period.
515
516 3. Insertion replacing part of a subtree that we haven't yet entered. This
517 may involve replacement of part of that subtree - but that won't affect
518 the iteration as we won't have reached the pointer to it yet and the
519 ancestry blocks are not replaced (the layout of those does not change).
520
521 4. Insertion replacing nodes that we're actively processing. This isn't a
522 problem as we've passed the anchoring pointer and won't switch onto the
523 new layout until we follow the back pointers - at which point we've
524 already examined the leaves in the replaced node (we iterate over all the
525 leaves in a node before following any of its metadata pointers).
526
527 We might, however, re-see some leaves that have been split out into a new
528 branch that's in a slot further along than we were at.
529
530 5. Insertion replacing nodes that we're processing a dependent branch of.
531 This won't affect us until we follow the back pointers. Similar to (4).
532
533 6. Deletion collapsing a branch under us. This doesn't affect us because the
534 back pointers will get us back to the parent of the new node before we
535 could see the new node. The entire collapsed subtree is thrown away
536 unchanged - and will still be rooted on the same slot, so we shouldn't
537 process it a second time as we'll go back to slot + 1.
538
539 .. note::
540
541 Under some circumstances, we need to simultaneously change the parent
542 pointer and the parent slot pointer on a node (say, for example, we
543 inserted another node before it and moved it up a level). We cannot do
544 this without locking against a read - so we have to replace that node too.
545
546 However, when we're changing a shortcut into a node this isn't a problem
547 as shortcuts only have one slot and so the parent slot number isn't used
548 when traversing backwards over one. This means that it's okay to change
549 the slot number first - provided suitable barriers are used to make sure
550 the parent slot number is read after the back pointer.
551
552 Obsolete blocks and leaves are freed up after an RCU grace period has passed,
553 so as long as anyone doing walking or iteration holds the RCU read lock, the
554 old superstructure should not go away on them.
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