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61009379 MD |
1 | RCU Judy Array Design |
2 | Mathieu Desnoyers <mathieu.desnoyers@efficios.com> | |
3 | March 8, 2012 | |
4 | ||
5 | Initial ideas based on the released Judy Shop Manual | |
6 | (http://judy.sourceforge.net/). Judy was invented by Doug Baskins and | |
7 | implemented by Hewlett-Packard. | |
8 | ||
9 | Thresholds and RCU-specific analysis is introduced in this document. | |
10 | ||
11 | Advantages of using Judy Array (compressed nodes) for RCU tree: | |
12 | - no rebalancing | |
13 | - no transplant | |
14 | - RCU-friendly! | |
15 | - favor cache-line alignment of structures | |
16 | ||
17 | Disadvantage: | |
18 | - updates that need to reallocate nodes are slower than, e.g. non-rcu | |
19 | red-black trees. | |
20 | ||
21 | Choice: Using 256 entries intermediate nodes (index can be represented | |
22 | on 8 bits): 4 levels on 32-bit, 8 levels on 64-bit | |
23 | ||
24 | ||
25 | * Node types (from less dense node to most dense) | |
26 | ||
27 | ||
28 | - empty node: | |
29 | ||
30 | Parent pointer is NULL. | |
31 | ||
32 | ||
33 | - Type A: sequential search in value and pointer arrays | |
34 | ||
35 | + Add/removal just needs to update value and pointer array, single-entry | |
36 | (non-RCU...). For RCU, we might need to update the entire node anyway. | |
37 | - Requires sequential search through all value array for lookup fail | |
38 | test. | |
39 | ||
40 | Filled at 3 entries max 64-bit | |
41 | 8 bits indicating number of children | |
42 | Array of 8-bit values followed by array of associated pointers. | |
43 | 64-bit: 1 byte + 3 bytes + 4 bytes pad + 3*8 = 32 bytes | |
44 | ||
45 | -> up to this point on 64-bit, sequential lookup and pointer read fit in | |
46 | a 32-byte cache line. | |
47 | - lookup fail&success: 1 cache-line. | |
48 | ||
49 | Filled at 6 entries max 32-bit, 7 entries max 64-bit | |
50 | 8 bits indicating number of children | |
51 | Array of 8-bit values followed by array of associated pointers. | |
52 | 32-bit: 1 byte + 6 bytes + 1 byte pad + 6*4bytes = 32 bytes | |
53 | 64-bit: 1 byte + 7 bytes + 7*8 = 64 bytes | |
54 | ||
55 | -> up to this point on 32-bit, sequential lookup and pointer read fit in | |
56 | a 32-byte cache line. | |
57 | - lookup fail&success: 1 cache-line. | |
58 | ||
59 | Filled at 12 entries max 32-bit, 14 entries max 64-bit | |
60 | 8 bits indicating number of children | |
61 | Array of 8-bit values followed by array of associated pointers. | |
62 | 32-bit: 1 byte + 12 bytes + 3 bytes pad + 12*4bytes = 64 bytes | |
63 | 64-bit: 1 byte + 14 bytes + 1 byte pad + 14*8 = 128 bytes | |
64 | ||
65 | Filled at 25 entries max 32-bit, 28 entries max 64-bit | |
66 | 8 bits indicating number of children | |
67 | Array of 8-bit values followed by array of associated pointers. | |
68 | 32-bit: 1 byte + 25 bytes + 2 bytes pad + 25*4bytes = 128 bytes | |
69 | 64-bit: 1 byte + 28 bytes + 3 bytes pad + 28*8 = 256 bytes | |
70 | ||
71 | ---> up to this point, on both 32-bit and 64-bit, the sequential lookup | |
72 | in values array fits in a 32-byte cache line. | |
73 | - lookup failure: 1 cache line. | |
74 | - lookup success: 2 cache lines. | |
75 | ||
76 | The two below are listed for completeness sake, but because they require | |
77 | 2 32-byte cache lines for lookup, these are deemed inappropriate. | |
78 | ||
79 | Filled at 51 entries max 32-bit, 56 entries max 64-bit | |
80 | 8 bits indicating number of children | |
81 | Array of 8-bit values followed by array of associated pointers. | |
82 | 32-bit: 1 byte + 51 bytes + 51*4bytes = 256 bytes | |
83 | 64-bit: 1 byte + 56 bytes + 7 bytes pad + 56*8 = 512 bytes | |
84 | ||
85 | Filled at 102 entries max 32-bit, 113 entries max 64-bit | |
86 | 8 bits indicating number of children | |
87 | Array of 8-bit values followed by array of associated pointers. | |
88 | 32-bit: 1 byte + 102 bytes + 1 byte pad + 102*4bytes = 512 bytes | |
89 | 64-bit: 1 byte + 113 bytes + 6 bytes pad + 113*8 = 1024 bytes | |
90 | ||
91 | ||
92 | - Type B: bitmap, followed by pointers array. | |
93 | ||
94 | bitmask (256 entries -> 256 bits -> 32 bytes) of populated children | |
95 | followed by an array of children pointers, in same order as appears in | |
96 | the bitmask | |
97 | ||
98 | + Allows lookup failure to use 32-byte cache-line only. (1 cacheline) | |
99 | + Allows lookup success to use 32-byte cache-line (bitmap), | |
100 | followed by direct lookup into pointer array. (2 cachelines) | |
101 | ||
102 | Filled at 8 entries 32-bit, 12 entries 64-bit | |
103 | 32-bit: 32 + (4*8) -> 64 bytes | |
104 | 64-bit: 32 + (8*12) -> 128 bytes | |
105 | ||
106 | Filled at 24 entries 32-bit, 28 entries 64-bit | |
107 | 32-bit: 32 + (4*24) -> 128 bytes | |
108 | 64-bit: 32 + (8*28) -> 256 bytes | |
109 | ||
110 | Filled at 56 entries 32-bit, 60 entries 64-bit | |
111 | 32-bit: 32 + (4*56) -> 256 bytes | |
112 | 64-bit: 32 + (8*60) -> 512 bytes | |
113 | ||
114 | Filled at 120 entries 32-bit, 124 entries 64-bit | |
115 | 32-bit: 32 + (4*95) -> 512 bytes | |
116 | 64-bit: 32 + (8*124) -> 1024 bytes | |
117 | ||
118 | ||
119 | - Type C: pigeon-hole array | |
120 | ||
121 | Filled at 47.2%/48.8% or more (32-bit: 121 entries+, 64-bit: 125 entries+) | |
122 | Array of children node pointers. Pointers NULL if no child at index. | |
123 | 32-bit: 4*256 = 1024 bytes | |
124 | 64-bit: 8*256 = 2048 bytes | |
125 | ||
126 | ||
127 | * Analysis of the thresholds: | |
128 | ||
129 | Analysis of number of cache-lines touched for each node, per-node-type, | |
130 | depending on the number of children per node, as we increment the number | |
131 | of children from 0 to 256. Through this, we choose number of children | |
132 | thresholds at which it is worthwhile to use a different node type. | |
133 | ||
134 | Per node: | |
135 | ||
136 | - ALWAYS 1 cache line hit for lookup failure (all cases) | |
137 | ||
138 | 32-bit | |
139 | ||
140 | - Unexisting | |
141 | ||
142 | 0 children | |
143 | ||
144 | - Type A: sequential search in value and pointer arrays | |
145 | - 1 cache line hit for lookup success | |
146 | - 32 bytes storage | |
147 | ||
148 | up to 6 children | |
149 | ||
150 | - 2 cache line hit for lookup success | |
151 | - 64 bytes storage | |
152 | ||
153 | up to 12 children | |
154 | ||
155 | - Type B: bitmap, followed by pointers array. | |
156 | - 2 cache line hit for lookup success | |
157 | - 128 bytes storage | |
158 | ||
159 | up to 24 children | |
160 | ||
161 | - 256 bytes storage | |
162 | up to 56 children | |
163 | ||
164 | - 512 bytes storage | |
165 | up to 120 children | |
166 | ||
167 | - Type C: pigeon-hole array | |
168 | - 1 cache line hit for lookup success | |
169 | - 1024 bytes storage | |
170 | ||
171 | up to 256 children | |
172 | ||
173 | ||
174 | 64-bit | |
175 | ||
176 | - Unexisting | |
177 | ||
178 | 0 children | |
179 | ||
180 | - Type A: sequential search in value and pointer arrays | |
181 | - 1 cache line hit for lookup success | |
182 | - 32 bytes storage | |
183 | ||
184 | up to 3 children | |
185 | ||
186 | - 2 cache line hit for lookup success | |
187 | - 64 bytes storage | |
188 | ||
189 | up to 7 children | |
190 | ||
191 | - 128 bytes storage | |
192 | ||
193 | up to 14 children | |
194 | ||
195 | - Type B: bitmap, followed by pointers array. | |
196 | - 2 cache line hit for lookup success | |
197 | - 256 bytes storage | |
198 | ||
199 | up to 28 children | |
200 | ||
201 | - 512 bytes storage | |
202 | up to 60 children | |
203 | ||
204 | - 1024 bytes storage | |
205 | up to 124 children | |
206 | ||
207 | - Type C: pigeon-hole array | |
208 | - 1 cache line hit for lookup success | |
209 | - 2048 bytes storage | |
210 | ||
211 | up to 256 children | |
212 | ||
213 | ||
214 | * Analysis of node type encoding and node pointers: | |
215 | ||
216 | Lookups are _always_ from the top of the tree going down. This | |
217 | facilitates RCU replacement as we only keep track of pointers going | |
218 | downward. | |
219 | ||
220 | Type of node encoded in the parent's pointer. Need to reserve 2 | |
221 | least-significant bits. | |
222 | ||
223 | Types of children: | |
224 | ||
225 | enum child_type { | |
e5227865 MD |
226 | RCU_JA_LINEAR = 0, /* Type A */ |
227 | /* 32-bit: 1 to 12 children, 8 to 64 bytes */ | |
228 | /* 64-bit: 1 to 14 children, 16 to 128 bytes */ | |
229 | RCU_JA_BITMAP = 1, /* Type B */ | |
61009379 MD |
230 | /* 32-bit: 13 to 120 children, 128 to 512 bytes */ |
231 | /* 64-bit: 15 to 124 children, 256 to 1024 bytes */ | |
e5227865 | 232 | RCU_JA_PIGEON = 2, /* Type C */ |
61009379 MD |
233 | /* 32-bit: 121 to 256 children, 1024 bytes */ |
234 | /* 64-bit: 125 to 256 children, 2048 bytes */ | |
e5227865 | 235 | /* Leaf nodes are implicit from their height in the tree */ |
61009379 MD |
236 | }; |
237 | ||
238 | If entire pointer is NULL, children is empty. | |
239 | ||
240 | ||
241 | * Lookup and Update Algorithms | |
242 | ||
243 | Let's propose a quite simple scheme that uses a mutex on nodes to manage | |
244 | update concurrency. It's certainly not optimal in terms of concurrency | |
245 | management within a node, but it has the advantage of being simple to | |
246 | implement and understand. | |
247 | ||
248 | We need to keep a count of the number of children nodes (for each node), | |
249 | to keep track of when the node type thresholds are reached. It would be | |
250 | important to put an hysteresis loop so we don't change between node | |
251 | types too often for a loop on add/removal of the same node. | |
252 | ||
253 | We acquire locks from child to parent, nested. We take all locks | |
254 | required to perform a given update in the tree (but no more) to keep it | |
255 | consistent with respect to number of children per node. | |
256 | ||
257 | If check for node being gc'd (always under node lock) fails, we simply | |
258 | need to release the lock and lookup the node again. | |
259 | ||
260 | ||
261 | - Leaf lookup | |
262 | ||
263 | rcu_read_lock() | |
264 | ||
265 | RCU-lookup each level of the tree. If level is not populated, fail. | |
266 | Until we reach the leaf node. | |
267 | ||
268 | rcu_read_unlock() | |
269 | ||
270 | ||
271 | - Leaf insertion | |
272 | ||
273 | A) Lookup | |
274 | ||
275 | rcu_read_lock() | |
276 | RCU-lookup insert position. Find location in tree where nodes are | |
277 | missing for this insertion. If leaf is already present, insert fails, | |
278 | releasing the rcu read lock. The insert location consists of a parent | |
279 | node to which we want to attach a new node. | |
280 | ||
281 | B) Lock | |
282 | ||
283 | RCU-lookup parent node. Take the parent lock. If the parent needs to be | |
284 | reallocated to make room for this insertion, RCU-lookup parent-parent | |
285 | node and take the parent-parent lock. For each lock taken, check if | |
286 | node is being gc'd. If gc'd, release lock, re-RCU-lookup this node, and | |
287 | retry. | |
288 | ||
289 | C) Create | |
290 | ||
291 | Construct the whole branch from the new topmost intermediate node down | |
292 | to the new leaf node we are inserting. | |
293 | ||
294 | D) Populate: | |
295 | - If parent node reallocation is needed: | |
296 | Reallocate the parent node, adding the new branch to it, and | |
297 | increment its node count. | |
298 | set gc flag in old nodes. | |
299 | call_rcu free for all old nodes. | |
300 | Populate new parent node with rcu_assign_pointer. | |
301 | - Else: | |
302 | Increment parent node count. | |
303 | Use rcu_assign_pointer to populate this new branch into the parent | |
304 | node. | |
305 | ||
306 | E) Locks | |
307 | ||
308 | Release parent and (if taken) parent-parent locks. | |
309 | rcu_read_unlock() | |
310 | ||
311 | ||
312 | - Leaf removal | |
313 | ||
314 | A) Lookup | |
315 | ||
316 | rcu_read_lock() | |
317 | RCU-lookup leaf to remove. If leaf is missing, fail and release rcu | |
318 | read lock. | |
319 | ||
320 | B) Lock | |
321 | ||
322 | RCU-lookup parent. Take the parent lock. If the parent needs to be | |
323 | reallocated because it would be too large for the decremented number of | |
324 | children, RCU-lookup parent-parent and take the parent-parent lock. Do | |
325 | so recursively until no node reallocation is needed, or until root is | |
326 | reached. | |
327 | ||
328 | For each lock taken, check if node is being gc'd. If gc'd, release lock, | |
329 | re-RCU-lookup this node, and retry. | |
330 | ||
331 | C) Create | |
332 | ||
333 | The branch (or portion of branch) consisting of taken locks necessarily | |
334 | has a simple node removal or update as operation to do on its top node. | |
335 | ||
336 | If the operation is a node removal, then, necessarily, the entire branch | |
337 | under the node removal operation will simply disappear. No node | |
338 | allocation is needed. | |
339 | ||
340 | Else, if the operation is a child node reallocation, the child node will | |
341 | necessarily do a node removal. So _its_ entire child branch will | |
342 | disappear. So reallocate this child node without the removed branch | |
343 | (remember to decrement its nr children count). | |
344 | ||
345 | D) Populate | |
346 | ||
347 | No reallocation case: simply set the appropriate child pointer in the | |
348 | topmost locked node to NULL. Decrement its nr children count. | |
349 | ||
350 | Reallocation case: set the child pointer in the topmost locked node to | |
351 | the newly allocated node. | |
352 | set old nodes gc flag. | |
353 | call_rcu free for all old nodes. | |
354 | ||
355 | E) Locks | |
356 | ||
357 | Release all locks. | |
358 | rcu_read_unlock() | |
359 | ||
360 | ||
361 | For the various types of nodes: | |
362 | ||
363 | - sequential search (type A) | |
364 | - RCU replacement: mutex | |
365 | - Entry update: mutex | |
366 | ||
367 | - bitmap followed by pointer array (type B) | |
368 | - RCU replacement: mutex | |
369 | - Entry update: mutex | |
370 | ||
371 | - pigeon hole array (type C) | |
372 | - RCU replacement: mutex | |
373 | - Entry update: mutex |