Local Linearizability

Transcription

1 Local Linearizability joint work with: Andreas Haas Andreas Holzer Michael Lippautz Ali Sezgin Tom Henzinger Christoph Kirsch Hannes Payer Helmut Veith

2 Concurrent Data Structures Correctness and Performance

3 Semantics of concurrent data structures t1: enq(2) deq(1) t2: enq(1) deq(2) e.g. pools, queues, stacks Sequential specification = set of legal sequences Consistency condition = e.g. linearizability / sequential consistency e.g. queue legal sequence enq(1)enq(2)deq(1)deq(2) e.g. the concurrent history above is a linearizable queue concurrent history

4 Consistency conditions there exists a legal sequence that preserves precedence Linearizability [Herlihy,Wing 90] 2 3 t1: enq(2) deq(1) t2: 1 enq(1) deq(2) 4 Sequential Consistency [Lamport 79] there exists a legal sequence that preserves per-thread precedence (program order) t1: 1enq(1) deq(2) t2: deq(1) enq(2) 2 3 4

5 Performance and scalability :-))) throughput :-) :-( :-\ # of threads / cores

6 Relaxations allow trading correctness for performance provide the potential for better-performing implementations

7 Relaxing the Semantics not sequentially correct Quantitative relaxations Henzinger, Kirsch, Payer, Sezgin,S. POPL13 Sequential specification = set of legal sequences Consistency condition = e.g. linearizability / sequential consistency for queues only (feel free to ask for more) too weak Local linearizability in this talk

8 Local Linearizability main idea Already present in some shared-memory consistency conditions (not in our form of choice) Partition a history into a set of local histories Require linearizability per local history no global witness Local sequential consistency is also possible

9 Local Linearizability (queue) example (sequential) history not linearizable t1: enq(1) deq(2) t2: enq(2) deq(1) t2-induced history, linearizable t1-induced history, linearizable locally linearizable

10 Local Linearizability (queue) definition Queue signature = {enq(x) x V} {deq(x) x V} {deq(empty)} For a history h with a thread T, we put IT = {enq(x) T h x V} in-methods of thread T are enqueues performed by thread T OT = {deq(x) T h enq(x) T IT} {deq(empty)} out-methods of thread T are dequeues (performed by any thread) corresponding to enqueues that are in-methods h is locally linearizable iff every thread-induced history ht= h (IT OT) is linearizable.

11 Local Linearizability for Container-Type DS Signature = Ins Rem SOb DOb For a history h with a thread T, we put IT = {m T h m Ins} in-methods of thread T are inserts performed by thread T OT = {m(a) h Rem i(a) T IT} {m(e) e Emp} {m(a) h DOb i(a) T IT} out-methods of thread T are removes and data-observations (performed by any thread) corresponding to in-methods h is locally linearizable iff every thread-induced history ht= h (IT OT) is linearizable.

12 Where do we stand? In general Linearizability Local Linearizability Sequential Consistency

13 Where do we stand? For queues (and most container-type data structures) Linearizability Local Linearizability Sequential Consistency

14 Properties Local linearizability is compositional like linearizability unlike sequential consistency h (over multiple objects) is locally linearizable iff each per-object subhistory of h is locally linearizable Local linearizability is modular / decompositional uses decomposition into smaller histories, by definition may allow for modular verification

15 Verification (queue) Queue sequential specification (axiomatic) s is a legal queue sequence iff 1. s is a legal pool sequence, and 2. enq(x) <s enq(y) deq(y) s deq(x) s deq(x) <s deq(y) Queue linearizability (axiomatic) Henzinger, Sezgin, Vafeiadis CONCUR13 h is queue linearizable iff 1. h is pool linearizable, and 2. enq(x) <h enq(y) deq(y) h deq(x) h deq(y) h deq(x) precedence order

16 Verification (queue) Queue sequential specification (axiomatic) s is a legal queue sequence iff 1. s is a legal pool sequence, and 2. enq(x) <s enq(y) deq(y) s deq(x) s deq(x) <s deq(y) Queue local linearizability (axiomatic) h is queue locally linearizable iff 1. h is pool locally linearizable, and 2. enq(x) <h i enq(y) deq(y) h deq(x) h deq(y) h deq(x) thread-local precedence order

17 Generic Implementations Your favorite linearizable data structure implementation Φ turns into a locally linearizable implementation by: t1 t2 tn segment of possibly dynamic size (n) LLD Φ (locally linearizable) Φ Φ Φ LL+D Φ local inserts / global (randomly distributed) removes (also pool linearizable)

18 million operations per sec (more is better) Performance number of threads LL+D MS queue performs significantly better than MS queue MS LCRQ k-fifo LL+D MS LLD LCRQ LLD k-fifo 1-RA DQ (a) Queues, LL queues, and queue-like pools

19 million operations per sec (more is better) Performance number of threads LLD Φ performs significantly better than Φ MS LCRQ k-fifo LL+D MS LLD LCRQ LLD k-fifo 1-RA DQ (a) Queues, LL queues, and queue-like pools

20 million operations per sec (more is better) Performance number of threads LL+D MS queue performs better than the best known pools MS LCRQ k-fifo LL+D MS LLD LCRQ LLD k-fifo 1-RA DQ (a) Queues, LL queues, and queue-like pools

21 Thank You! Local Linearizability joint work with: Andreas Haas Andreas Holzer Michael Lippautz Ali Sezgin Tom Henzinger Christoph Kirsch Hannes Payer Helmut Veith

22 Thank You! Local Linearizability joint work with: Andreas Haas Andreas Holzer Michael Lippautz Ali Sezgin Tom Henzinger Christoph Kirsch Hannes Payer Helmut Veith