1		   ========================================
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 *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
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.
575