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David Howells3cb98952013-09-24 10:35:17 +01001 ========================================
2 GENERIC ASSOCIATIVE ARRAY IMPLEMENTATION
3 ========================================
4
5Contents:
6
7 - Overview.
8
9 - The public API.
10 - Edit script.
11 - Operations table.
12 - Manipulation functions.
13 - Access functions.
14 - Index key form.
15
16 - Internal workings.
17 - Basic internal tree layout.
18 - Shortcuts.
19 - Splitting and collapsing nodes.
20 - Non-recursive iteration.
21 - Simultaneous alteration and iteration.
22
23
24========
25OVERVIEW
26========
27
28This associative array implementation is an object container with the following
29properties:
30
31 (1) Objects are opaque pointers. The implementation does not care where they
32 point (if anywhere) or what they point to (if anything).
33
34 [!] NOTE: Pointers to objects _must_ be zero in the least significant bit.
35
36 (2) Objects do not need to contain linkage blocks for use by the array. This
37 permits an object to be located in multiple arrays simultaneously.
38 Rather, the array is made up of metadata blocks that point to objects.
39
40 (3) Objects require index keys to locate them within the array.
41
42 (4) Index keys must be unique. Inserting an object with the same key as one
43 already in the array will replace the old object.
44
45 (5) Index keys can be of any length and can be of different lengths.
46
47 (6) Index keys should encode the length early on, before any variation due to
48 length is seen.
49
50 (7) Index keys can include a hash to scatter objects throughout the array.
51
52 (8) The array can iterated over. The objects will not necessarily come out in
53 key order.
54
55 (9) The array can be iterated over whilst it is being modified, provided the
56 RCU readlock is being held by the iterator. Note, however, under these
57 circumstances, some objects may be seen more than once. If this is a
58 problem, the iterator should lock against modification. Objects will not
59 be missed, however, unless deleted.
60
61(10) Objects in the array can be looked up by means of their index key.
62
63(11) Objects can be looked up whilst the array is being modified, provided the
64 RCU readlock is being held by the thread doing the look up.
65
66The implementation uses a tree of 16-pointer nodes internally that are indexed
67on each level by nibbles from the index key in the same manner as in a radix
68tree. To improve memory efficiency, shortcuts can be emplaced to skip over
69what would otherwise be a series of single-occupancy nodes. Further, nodes
70pack leaf object pointers into spare space in the node rather than making an
71extra branch until as such time an object needs to be added to a full node.
72
73
74==============
75THE PUBLIC API
76==============
77
78The public API can be found in <linux/assoc_array.h>. The associative array is
79rooted on the following structure:
80
81 struct assoc_array {
82 ...
83 };
84
85The code is selected by enabling CONFIG_ASSOCIATIVE_ARRAY.
86
87
88EDIT SCRIPT
89-----------
90
91The insertion and deletion functions produce an 'edit script' that can later be
92applied to effect the changes without risking ENOMEM. This retains the
93preallocated metadata blocks that will be installed in the internal tree and
94keeps track of the metadata blocks that will be removed from the tree when the
95script is applied.
96
97This is also used to keep track of dead blocks and dead objects after the
98script has been applied so that they can be freed later. The freeing is done
99after an RCU grace period has passed - thus allowing access functions to
100proceed under the RCU read lock.
101
102The script appears as outside of the API as a pointer of the type:
103
104 struct assoc_array_edit;
105
106There are two functions for dealing with the script:
107
108 (1) Apply an edit script.
109
110 void assoc_array_apply_edit(struct assoc_array_edit *edit);
111
112 This will perform the edit functions, interpolating various write barriers
113 to permit accesses under the RCU read lock to continue. The edit script
114 will then be passed to call_rcu() to free it and any dead stuff it points
115 to.
116
117 (2) Cancel an edit script.
118
119 void assoc_array_cancel_edit(struct assoc_array_edit *edit);
120
121 This frees the edit script and all preallocated memory immediately. If
122 this was for insertion, the new object is _not_ released by this function,
123 but must rather be released by the caller.
124
125These functions are guaranteed not to fail.
126
127
128OPERATIONS TABLE
129----------------
130
131Various functions take a table of operations:
132
133 struct assoc_array_ops {
134 ...
135 };
136
137This points to a number of methods, all of which need to be provided:
138
139 (1) Get a chunk of index key from caller data:
140
141 unsigned long (*get_key_chunk)(const void *index_key, int level);
142
143 This should return a chunk of caller-supplied index key starting at the
144 *bit* position given by the level argument. The level argument will be a
145 multiple of ASSOC_ARRAY_KEY_CHUNK_SIZE and the function should return
146 ASSOC_ARRAY_KEY_CHUNK_SIZE bits. No error is possible.
147
148
149 (2) Get a chunk of an object's index key.
150
151 unsigned long (*get_object_key_chunk)(const void *object, int level);
152
153 As the previous function, but gets its data from an object in the array
154 rather than from a caller-supplied index key.
155
156
157 (3) See if this is the object we're looking for.
158
159 bool (*compare_object)(const void *object, const void *index_key);
160
161 Compare the object against an index key and return true if it matches and
162 false if it doesn't.
163
164
165 (4) Diff the index keys of two objects.
166
167 int (*diff_objects)(const void *a, const void *b);
168
169 Return the bit position at which the index keys of two objects differ or
170 -1 if they are the same.
171
172
173 (5) Free an object.
174
175 void (*free_object)(void *object);
176
177 Free the specified object. Note that this may be called an RCU grace
178 period after assoc_array_apply_edit() was called, so synchronize_rcu() may
179 be necessary on module unloading.
180
181
182MANIPULATION FUNCTIONS
183----------------------
184
185There are a number of functions for manipulating an associative array:
186
187 (1) Initialise an associative array.
188
189 void assoc_array_init(struct assoc_array *array);
190
191 This initialises the base structure for an associative array. It can't
192 fail.
193
194
195 (2) Insert/replace an object in an associative array.
196
197 struct assoc_array_edit *
198 assoc_array_insert(struct assoc_array *array,
199 const struct assoc_array_ops *ops,
200 const void *index_key,
201 void *object);
202
203 This inserts the given object into the array. Note that the least
204 significant bit of the pointer must be zero as it's used to type-mark
205 pointers internally.
206
207 If an object already exists for that key then it will be replaced with the
208 new object and the old one will be freed automatically.
209
210 The index_key argument should hold index key information and is
211 passed to the methods in the ops table when they are called.
212
213 This function makes no alteration to the array itself, but rather returns
214 an edit script that must be applied. -ENOMEM is returned in the case of
215 an out-of-memory error.
216
217 The caller should lock exclusively against other modifiers of the array.
218
219
220 (3) Delete an object from an associative array.
221
222 struct assoc_array_edit *
223 assoc_array_delete(struct assoc_array *array,
224 const struct assoc_array_ops *ops,
225 const void *index_key);
226
227 This deletes an object that matches the specified data from the array.
228
229 The index_key argument should hold index key information and is
230 passed to the methods in the ops table when they are called.
231
232 This function makes no alteration to the array itself, but rather returns
233 an edit script that must be applied. -ENOMEM is returned in the case of
234 an out-of-memory error. NULL will be returned if the specified object is
235 not found within the array.
236
237 The caller should lock exclusively against other modifiers of the array.
238
239
240 (4) Delete all objects from an associative array.
241
242 struct assoc_array_edit *
243 assoc_array_clear(struct assoc_array *array,
244 const struct assoc_array_ops *ops);
245
246 This deletes all the objects from an associative array and leaves it
247 completely empty.
248
249 This function makes no alteration to the array itself, but rather returns
250 an edit script that must be applied. -ENOMEM is returned in the case of
251 an out-of-memory error.
252
253 The caller should lock exclusively against other modifiers of the array.
254
255
256 (5) Destroy an associative array, deleting all objects.
257
258 void assoc_array_destroy(struct assoc_array *array,
259 const struct assoc_array_ops *ops);
260
261 This destroys the contents of the associative array and leaves it
262 completely empty. It is not permitted for another thread to be traversing
263 the array under the RCU read lock at the same time as this function is
264 destroying it as no RCU deferral is performed on memory release -
265 something that would require memory to be allocated.
266
267 The caller should lock exclusively against other modifiers and accessors
268 of the array.
269
270
271 (6) Garbage collect an associative array.
272
273 int assoc_array_gc(struct assoc_array *array,
274 const struct assoc_array_ops *ops,
275 bool (*iterator)(void *object, void *iterator_data),
276 void *iterator_data);
277
278 This iterates over the objects in an associative array and passes each one
279 to iterator(). If iterator() returns true, the object is kept. If it
280 returns false, the object will be freed. If the iterator() function
281 returns true, it must perform any appropriate refcount incrementing on the
282 object before returning.
283
284 The internal tree will be packed down if possible as part of the iteration
285 to reduce the number of nodes in it.
286
287 The iterator_data is passed directly to iterator() and is otherwise
288 ignored by the function.
289
290 The function will return 0 if successful and -ENOMEM if there wasn't
291 enough memory.
292
293 It is possible for other threads to iterate over or search the array under
294 the RCU read lock whilst this function is in progress. The caller should
295 lock exclusively against other modifiers of the array.
296
297
298ACCESS FUNCTIONS
299----------------
300
301There are two functions for accessing an associative array:
302
303 (1) Iterate over all the objects in an associative array.
304
305 int assoc_array_iterate(const struct assoc_array *array,
306 int (*iterator)(const void *object,
307 void *iterator_data),
308 void *iterator_data);
309
310 This passes each object in the array to the iterator callback function.
311 iterator_data is private data for that function.
312
313 This may be used on an array at the same time as the array is being
314 modified, provided the RCU read lock is held. Under such circumstances,
315 it is possible for the iteration function to see some objects twice. If
316 this is a problem, then modification should be locked against. The
317 iteration algorithm should not, however, miss any objects.
318
319 The function will return 0 if no objects were in the array or else it will
320 return the result of the last iterator function called. Iteration stops
321 immediately if any call to the iteration function results in a non-zero
322 return.
323
324
325 (2) Find an object in an associative array.
326
327 void *assoc_array_find(const struct assoc_array *array,
328 const struct assoc_array_ops *ops,
329 const void *index_key);
330
331 This walks through the array's internal tree directly to the object
332 specified by the index key..
333
334 This may be used on an array at the same time as the array is being
335 modified, provided the RCU read lock is held.
336
337 The function will return the object if found (and set *_type to the object
338 type) or will return NULL if the object was not found.
339
340
341INDEX KEY FORM
342--------------
343
344The index key can be of any form, but since the algorithms aren't told how long
345the key is, it is strongly recommended that the index key includes its length
346very early on before any variation due to the length would have an effect on
347comparisons.
348
349This will cause leaves with different length keys to scatter away from each
350other - and those with the same length keys to cluster together.
351
352It is also recommended that the index key begin with a hash of the rest of the
353key to maximise scattering throughout keyspace.
354
355The better the scattering, the wider and lower the internal tree will be.
356
357Poor scattering isn't too much of a problem as there are shortcuts and nodes
358can contain mixtures of leaves and metadata pointers.
359
360The index key is read in chunks of machine word. Each chunk is subdivided into
361one nibble (4 bits) per level, so on a 32-bit CPU this is good for 8 levels and
362on a 64-bit CPU, 16 levels. Unless the scattering is really poor, it is
363unlikely that more than one word of any particular index key will have to be
364used.
365
366
367=================
368INTERNAL WORKINGS
369=================
370
371The associative array data structure has an internal tree. This tree is
372constructed of two types of metadata blocks: nodes and shortcuts.
373
374A node is an array of slots. Each slot can contain one of four things:
375
376 (*) A NULL pointer, indicating that the slot is empty.
377
378 (*) A pointer to an object (a leaf).
379
380 (*) A pointer to a node at the next level.
381
382 (*) A pointer to a shortcut.
383
384
385BASIC INTERNAL TREE LAYOUT
386--------------------------
387
388Ignoring shortcuts for the moment, the nodes form a multilevel tree. The index
389key space is strictly subdivided by the nodes in the tree and nodes occur on
390fixed levels. For example:
391
392 Level: 0 1 2 3
393 =============== =============== =============== ===============
394 NODE D
395 NODE B NODE C +------>+---+
396 +------>+---+ +------>+---+ | | 0 |
397 NODE A | | 0 | | | 0 | | +---+
398 +---+ | +---+ | +---+ | : :
399 | 0 | | : : | : : | +---+
400 +---+ | +---+ | +---+ | | f |
401 | 1 |---+ | 3 |---+ | 7 |---+ +---+
402 +---+ +---+ +---+
403 : : : : | 8 |---+
404 +---+ +---+ +---+ | NODE E
405 | e |---+ | f | : : +------>+---+
406 +---+ | +---+ +---+ | 0 |
407 | f | | | f | +---+
408 +---+ | +---+ : :
409 | NODE F +---+
410 +------>+---+ | f |
411 | 0 | NODE G +---+
412 +---+ +------>+---+
413 : : | | 0 |
414 +---+ | +---+
415 | 6 |---+ : :
416 +---+ +---+
417 : : | f |
418 +---+ +---+
419 | f |
420 +---+
421
422In the above example, there are 7 nodes (A-G), each with 16 slots (0-f).
423Assuming no other meta data nodes in the tree, the key space is divided thusly:
424
425 KEY PREFIX NODE
426 ========== ====
427 137* D
428 138* E
429 13[0-69-f]* C
430 1[0-24-f]* B
431 e6* G
432 e[0-57-f]* F
433 [02-df]* A
434
435So, for instance, keys with the following example index keys will be found in
436the appropriate nodes:
437
438 INDEX KEY PREFIX NODE
439 =============== ======= ====
440 13694892892489 13 C
441 13795289025897 137 D
442 13889dde88793 138 E
443 138bbb89003093 138 E
444 1394879524789 12 C
445 1458952489 1 B
446 9431809de993ba - A
447 b4542910809cd - A
448 e5284310def98 e F
449 e68428974237 e6 G
450 e7fffcbd443 e F
451 f3842239082 - A
452
453To save memory, if a node can hold all the leaves in its portion of keyspace,
454then the node will have all those leaves in it and will not have any metadata
455pointers - even if some of those leaves would like to be in the same slot.
456
457A node can contain a heterogeneous mix of leaves and metadata pointers.
458Metadata pointers must be in the slots that match their subdivisions of key
459space. The leaves can be in any slot not occupied by a metadata pointer. It
460is guaranteed that none of the leaves in a node will match a slot occupied by a
461metadata pointer. If the metadata pointer is there, any leaf whose key matches
462the metadata key prefix must be in the subtree that the metadata pointer points
463to.
464
465In the above example list of index keys, node A will contain:
466
467 SLOT CONTENT INDEX KEY (PREFIX)
468 ==== =============== ==================
469 1 PTR TO NODE B 1*
470 any LEAF 9431809de993ba
471 any LEAF b4542910809cd
472 e PTR TO NODE F e*
473 any LEAF f3842239082
474
475and node B:
476
477 3 PTR TO NODE C 13*
478 any LEAF 1458952489
479
480
481SHORTCUTS
482---------
483
484Shortcuts are metadata records that jump over a piece of keyspace. A shortcut
485is a replacement for a series of single-occupancy nodes ascending through the
486levels. Shortcuts exist to save memory and to speed up traversal.
487
488It is possible for the root of the tree to be a shortcut - say, for example,
489the tree contains at least 17 nodes all with key prefix '1111'. The insertion
490algorithm will insert a shortcut to skip over the '1111' keyspace in a single
491bound and get to the fourth level where these actually become different.
492
493
494SPLITTING AND COLLAPSING NODES
495------------------------------
496
497Each node has a maximum capacity of 16 leaves and metadata pointers. If the
498insertion algorithm finds that it is trying to insert a 17th object into a
499node, that node will be split such that at least two leaves that have a common
500key segment at that level end up in a separate node rooted on that slot for
501that common key segment.
502
503If the leaves in a full node and the leaf that is being inserted are
504sufficiently similar, then a shortcut will be inserted into the tree.
505
506When the number of objects in the subtree rooted at a node falls to 16 or
507fewer, then the subtree will be collapsed down to a single node - and this will
508ripple towards the root if possible.
509
510
511NON-RECURSIVE ITERATION
512-----------------------
513
514Each node and shortcut contains a back pointer to its parent and the number of
515slot in that parent that points to it. None-recursive iteration uses these to
516proceed rootwards through the tree, going to the parent node, slot N + 1 to
517make sure progress is made without the need for a stack.
518
519The backpointers, however, make simultaneous alteration and iteration tricky.
520
521
522SIMULTANEOUS ALTERATION AND ITERATION
523-------------------------------------
524
525There are a number of cases to consider:
526
527 (1) Simple insert/replace. This involves simply replacing a NULL or old
528 matching leaf pointer with the pointer to the new leaf after a barrier.
529 The metadata blocks don't change otherwise. An old leaf won't be freed
530 until after the RCU grace period.
531
532 (2) Simple delete. This involves just clearing an old matching leaf. The
533 metadata blocks don't change otherwise. The old leaf won't be freed until
534 after the RCU grace period.
535
536 (3) Insertion replacing part of a subtree that we haven't yet entered. This
537 may involve replacement of part of that subtree - but that won't affect
538 the iteration as we won't have reached the pointer to it yet and the
539 ancestry blocks are not replaced (the layout of those does not change).
540
541 (4) Insertion replacing nodes that we're actively processing. This isn't a
542 problem as we've passed the anchoring pointer and won't switch onto the
543 new layout until we follow the back pointers - at which point we've
544 already examined the leaves in the replaced node (we iterate over all the
545 leaves in a node before following any of its metadata pointers).
546
547 We might, however, re-see some leaves that have been split out into a new
548 branch that's in a slot further along than we were at.
549
550 (5) Insertion replacing nodes that we're processing a dependent branch of.
551 This won't affect us until we follow the back pointers. Similar to (4).
552
553 (6) Deletion collapsing a branch under us. This doesn't affect us because the
554 back pointers will get us back to the parent of the new node before we
555 could see the new node. The entire collapsed subtree is thrown away
556 unchanged - and will still be rooted on the same slot, so we shouldn't
557 process it a second time as we'll go back to slot + 1.
558
559Note:
560
561 (*) Under some circumstances, we need to simultaneously change the parent
562 pointer and the parent slot pointer on a node (say, for example, we
563 inserted another node before it and moved it up a level). We cannot do
564 this without locking against a read - so we have to replace that node too.
565
566 However, when we're changing a shortcut into a node this isn't a problem
567 as shortcuts only have one slot and so the parent slot number isn't used
568 when traversing backwards over one. This means that it's okay to change
569 the slot number first - provided suitable barriers are used to make sure
570 the parent slot number is read after the back pointer.
571
572Obsolete blocks and leaves are freed up after an RCU grace period has passed,
573so as long as anyone doing walking or iteration holds the RCU read lock, the
574old superstructure should not go away on them.