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1 | ======================================== |
2 | GENERIC ASSOCIATIVE ARRAY IMPLEMENTATION |
3 | ======================================== |
4 | |
5 | Contents: |
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 | ======== |
25 | OVERVIEW |
26 | ======== |
27 | |
28 | This associative array implementation is an object container with the following |
29 | properties: |
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 | |
66 | The implementation uses a tree of 16-pointer nodes internally that are indexed |
67 | on each level by nibbles from the index key in the same manner as in a radix |
68 | tree. To improve memory efficiency, shortcuts can be emplaced to skip over |
69 | what would otherwise be a series of single-occupancy nodes. Further, nodes |
70 | pack leaf object pointers into spare space in the node rather than making an |
71 | extra branch until as such time an object needs to be added to a full node. |
72 | |
73 | |
74 | ============== |
75 | THE PUBLIC API |
76 | ============== |
77 | |
78 | The public API can be found in <linux/assoc_array.h>. The associative array is |
79 | rooted on the following structure: |
80 | |
81 | struct assoc_array { |
82 | ... |
83 | }; |
84 | |
85 | The code is selected by enabling CONFIG_ASSOCIATIVE_ARRAY. |
86 | |
87 | |
88 | EDIT SCRIPT |
89 | ----------- |
90 | |
91 | The insertion and deletion functions produce an 'edit script' that can later be |
92 | applied to effect the changes without risking ENOMEM. This retains the |
93 | preallocated metadata blocks that will be installed in the internal tree and |
94 | keeps track of the metadata blocks that will be removed from the tree when the |
95 | script is applied. |
96 | |
97 | This is also used to keep track of dead blocks and dead objects after the |
98 | script has been applied so that they can be freed later. The freeing is done |
99 | after an RCU grace period has passed - thus allowing access functions to |
100 | proceed under the RCU read lock. |
101 | |
102 | The script appears as outside of the API as a pointer of the type: |
103 | |
104 | struct assoc_array_edit; |
105 | |
106 | There 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 | |
125 | These functions are guaranteed not to fail. |
126 | |
127 | |
128 | OPERATIONS TABLE |
129 | ---------------- |
130 | |
131 | Various functions take a table of operations: |
132 | |
133 | struct assoc_array_ops { |
134 | ... |
135 | }; |
136 | |
137 | This 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 *object, const void *index_key); |
168 | |
169 | Return the bit position at which the index key of the specified object |
170 | differs from the given index key or -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 | |
182 | MANIPULATION FUNCTIONS |
183 | ---------------------- |
184 | |
185 | There 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 | |
298 | ACCESS FUNCTIONS |
299 | ---------------- |
300 | |
301 | There 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 | |
341 | INDEX KEY FORM |
342 | -------------- |
343 | |
344 | The index key can be of any form, but since the algorithms aren't told how long |
345 | the key is, it is strongly recommended that the index key includes its length |
346 | very early on before any variation due to the length would have an effect on |
347 | comparisons. |
348 | |
349 | This will cause leaves with different length keys to scatter away from each |
350 | other - and those with the same length keys to cluster together. |
351 | |
352 | It is also recommended that the index key begin with a hash of the rest of the |
353 | key to maximise scattering throughout keyspace. |
354 | |
355 | The better the scattering, the wider and lower the internal tree will be. |
356 | |
357 | Poor scattering isn't too much of a problem as there are shortcuts and nodes |
358 | can contain mixtures of leaves and metadata pointers. |
359 | |
360 | The index key is read in chunks of machine word. Each chunk is subdivided into |
361 | one nibble (4 bits) per level, so on a 32-bit CPU this is good for 8 levels and |
362 | on a 64-bit CPU, 16 levels. Unless the scattering is really poor, it is |
363 | unlikely that more than one word of any particular index key will have to be |
364 | used. |
365 | |
366 | |
367 | ================= |
368 | INTERNAL WORKINGS |
369 | ================= |
370 | |
371 | The associative array data structure has an internal tree. This tree is |
372 | constructed of two types of metadata blocks: nodes and shortcuts. |
373 | |
374 | A 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 | |
385 | BASIC INTERNAL TREE LAYOUT |
386 | -------------------------- |
387 | |
388 | Ignoring shortcuts for the moment, the nodes form a multilevel tree. The index |
389 | key space is strictly subdivided by the nodes in the tree and nodes occur on |
390 | fixed 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 | |
422 | In the above example, there are 7 nodes (A-G), each with 16 slots (0-f). |
423 | Assuming 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 | |
435 | So, for instance, keys with the following example index keys will be found in |
436 | the 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 | |
453 | To save memory, if a node can hold all the leaves in its portion of keyspace, |
454 | then the node will have all those leaves in it and will not have any metadata |
455 | pointers - even if some of those leaves would like to be in the same slot. |
456 | |
457 | A node can contain a heterogeneous mix of leaves and metadata pointers. |
458 | Metadata pointers must be in the slots that match their subdivisions of key |
459 | space. The leaves can be in any slot not occupied by a metadata pointer. It |
460 | is guaranteed that none of the leaves in a node will match a slot occupied by a |
461 | metadata pointer. If the metadata pointer is there, any leaf whose key matches |
462 | the metadata key prefix must be in the subtree that the metadata pointer points |
463 | to. |
464 | |
465 | In 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 | |
475 | and node B: |
476 | |
477 | 3 PTR TO NODE C 13* |
478 | any LEAF 1458952489 |
479 | |
480 | |
481 | SHORTCUTS |
482 | --------- |
483 | |
484 | Shortcuts are metadata records that jump over a piece of keyspace. A shortcut |
485 | is a replacement for a series of single-occupancy nodes ascending through the |
486 | levels. Shortcuts exist to save memory and to speed up traversal. |
487 | |
488 | It is possible for the root of the tree to be a shortcut - say, for example, |
489 | the tree contains at least 17 nodes all with key prefix '1111'. The insertion |
490 | algorithm will insert a shortcut to skip over the '1111' keyspace in a single |
491 | bound and get to the fourth level where these actually become different. |
492 | |
493 | |
494 | SPLITTING AND COLLAPSING NODES |
495 | ------------------------------ |
496 | |
497 | Each node has a maximum capacity of 16 leaves and metadata pointers. If the |
498 | insertion algorithm finds that it is trying to insert a 17th object into a |
499 | node, that node will be split such that at least two leaves that have a common |
500 | key segment at that level end up in a separate node rooted on that slot for |
501 | that common key segment. |
502 | |
503 | If the leaves in a full node and the leaf that is being inserted are |
504 | sufficiently similar, then a shortcut will be inserted into the tree. |
505 | |
506 | When the number of objects in the subtree rooted at a node falls to 16 or |
507 | fewer, then the subtree will be collapsed down to a single node - and this will |
508 | ripple towards the root if possible. |
509 | |
510 | |
511 | NON-RECURSIVE ITERATION |
512 | ----------------------- |
513 | |
514 | Each node and shortcut contains a back pointer to its parent and the number of |
515 | slot in that parent that points to it. None-recursive iteration uses these to |
516 | proceed rootwards through the tree, going to the parent node, slot N + 1 to |
517 | make sure progress is made without the need for a stack. |
518 | |
519 | The backpointers, however, make simultaneous alteration and iteration tricky. |
520 | |
521 | |
522 | SIMULTANEOUS ALTERATION AND ITERATION |
523 | ------------------------------------- |
524 | |
525 | There 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 | |
559 | Note: |
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 | |
572 | Obsolete blocks and leaves are freed up after an RCU grace period has passed, |
573 | so as long as anyone doing walking or iteration holds the RCU read lock, the |
574 | old superstructure should not go away on them. |
575 |
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