1. Algorithmics for Software Transactional Memory Hagit Attiya Technion

2. 2 Moore's Law is dead … says Gordon Moore (TechWorld, 4/2005) Intel announces a drastic change in its business strategy (San Francisco, 5/2004): «Multicore is the way to boost performance» Many applications will be concurrent Forking threads is easy, Handling the conflicts is hard!

3. 3 Transactional Synchronization A transaction is a sequence of operations by a single process on a set of data items (data set) to be executed atomically We consider only read/write operations:  Read set: the items read by T  Write set: the items written by T Read X Write X Read Z Read Y Read X Write X Read Z Read Y

4. 4 Transactional Synchronization A transaction is a sequence of operations by a single process on a set of data items (data set) to be executed atomically A transaction ends either by committing  all its updates take effect or by aborting  no update is effective Read X Write X Read Z Read Y Commit/ Abort Read X Write X Read Z Read Y Commit/ Abort

5. 5 Software Implementation of TM Data representation for transactions & data Algorithms to execute transactions in terms of low-level primitives (read, write, CAS…) on base objects (memory locations) Must provide Opacity [Guerroui & Kapalka] or strict serializability [Papadimitriou] Obstruction freedom

6. Typical Implementation Scheme To write data item O, a transaction acquires O, possibly aborting the transaction that owns O (killer write) To read an object, a transaction takes a snapshot to see if the system hasn’t changed since its previous reads; else T is aborted (careful read) Or: validate the reads when the transaction asks to commit (optimistic read)

7. 7 Algorithmics Acquiring several data items Validating that a set of values read is consistent Multi-location Synchronization Atomic Snapshot

8. 8 (Full) Atomic Snapshot [Afek et al. 1990] n components Update a single component Scan all the components “at once” (atomically) Provides an instantaneous view of the whole memory update ok scan v 1,…,v n

9. 9 Partial Snapshot [Attiya, Guerraoui, Ruppert, 2008] n components Update a single component Scan components “at once” (atomically) Allows to read parts of the memory Worthwhile if we can do it more efficiently than a (full) scan update ok scan v i1,…,v ir

10. 10 Optimizing Partial Scans Transactions that only observe the data  Empty write set Be invisible (not write to base objects)  Avoid contention for the memory Always terminate successfully (wait-free)

11. 11 DAP: Disjoint Access Parallelism T1T1 Read(Y) Write(X 1 ) T2T2 Write(X 2 ) T3T3 Read(X 2 ) Read(X 1 ) Disjoint data sets  no contention Data sets are connected  may contend Y X2X2 X1X1 T3T3 T1T1 Improves scalability for large data structures by reducing interference

12. 12 DAP: More Formally An STM implementation is disjoint access parallel if two transactions T 1 and T 2 access the same base object ONLY IF the data sets of T 1 and T 2 are connected. The data sets of T 1 & T 2 either intersect or are connected via other transactions

13. 13 State of the Art Read-only Tx termination Invisible read-only Tx DAPAlgorithm  [Herlihy, Luchangco, Moir & Scherer]  [Avni & Shavit]  [Riegel, Felber & Fetzer]  Harris, Fraser & Pratt]

14. 14 Inherent Tradeoff Theorem. There is no TM implementation that is DAP and has invisible & wait-free read-only transactions [Attiya, Hillel & Milani] Proof utilizes the notion of a flippable execution, used to prove lower bounds for atomic snapshot objects [Israeli, Shirazi] [Attiya, Ellen & Fatourou]

15. 15 Flippable Execution w/ 2 Updaters p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k A complete transaction in which p 1 writes l-1 to X 1 A read-only transaction by q that reads X 1, X 2 EkEk

16. 16 Flippable Execution w/ 2 Updaters p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k EkEk Indistinguishable from executions where the order of (each pair of) updates is flipped… In one of two ways (forward and backward).

17. 17 Flippable Execution: Backward Flip p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k EkEk p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k Backward Flip

18. 18 Lemma 1. The read-only transaction of q cannot terminate successfully Relies on strict serializabitly (linearizability)  Any interleaving of the transactions yields a result that can be achieved in a sequential execution of the same set of transactions (a serialization)  The serialization must preserve the real-time order of (non-overlapping) transactions Why Flippable Executions?

19. 19 Serialization of E k p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k EkEk U 1 … U l …U 0 U l-1 U k Serialization of E k : Possible serialization point Returns (l-1,l-2)

20. 20 Nowhere to Serialize p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k EkEk U 1 … U l …U 0 U l-1 U k Serialization Returns (l-1,l-2) p1p1 p2p2 q s 1 … s l-1 s l … s k U 1 … U l … U 0 … U l-1 … U k BW Flip Still returns (l-1,l-2) U 1 … U l U l-1 … U k U0U0 Serialization x Indistinguishable from some flip (say, backward) X 1 = l-2 X 2 = l-3 X 1 = l X 2 = l-3 X 1 = l X 2 = l-1

21. 21 Constructing a Flippable Execution Lemma 2. In a DAP TM, two consecutive transactions writing to different data items do not contend on the same base object. U1U1 U2U2

22. 22 Proof of Lemma 2 Towards a contradiction, assumme U 1 and U 2 contend on a base object Let o be the last base object accessed by U 1 for which U 2 has a contending access U1U1 U2U2 Last contending access to o First contending access to o

23. 23 Proof of Lemma 2 By contradictions, assumme U 1 and U 2 contend on a base object U1U1 U2U2 Last contending access to o First contending access to o U1U1 U2U2 U1 and U2 have disjoint data sets & contend on a base object Not DAP

24. 24 Completing the Proof Show that a flippable execution exists  The steps of the read-only transaction can be removed (since it is invisible)  Since their data sets are disjoint, transactions U l & U l-1 do not “communicate” (by Lemma 2)  Can be flipped  By Lemma 1, the read-only transaction cannot terminate successfully  If aborts, can apply the same argument again…

25. 25 Extensions… Also a Lower Bound: A transaction with a data set of size t must write to t-2 base objects The results hold also for weaker TM consistency conditions: Serializability Snapshot Isolation

26. 26 Algorithmics Acquiring several locations Validating that a set of values read is consistent Multi-location Synchronization Atomic Snapshot

27. 27 Multi-Location Synchronization Acquire nodes in the data set How to resolve conflicts with blocking operations (holding a required data item)?  To reduce delays

28. 28 Multi-Location Synchronization Acquire nodes in the data set How to resolve conflicts with blocking operations (holding a required data item)?  To reduce delays  To avoid deadlock

29. 29 Multi-Location Synchronization: Classical Solution E.g., [Touitou & Shavit] Acquired items by increasing order (e.g., of addresses) Avoids deadlocks But not delays Cannot be applied when data items are given in piecemeal… 2 5 6 8 10 13

30. 30 Multi-Location Synchronization: Practical STM Implementations Use a contention manager to decide which transaction has the object (the other aborts)  The other operation aborts & restarts But this requires support from the operating system Does not have provable guarantees

31. 31 Multi-Location Synchronization: More Concurrency [Attiya, Hillel] Acquire locks in arbitrary order  No need to know the data set in advance When there is a conflict between two transactions contending for a data item, either  Wait for the other operation  Abort & reset the other operation

32. 32 Distributed Conflict Resolution Depends on the operations’ progress The more advanced operation wins 1.How to gauge progress? 2.What to do on a tie?

33. 33 Who’s More Advanced? The operation that locked more data items If a less advanced operation needs an item  wait (blocking in a limited radius) or help the conflicting operation If a more advanced operation needs an item  abort the conflicting operation and claim the item

34. 34 What about Ties? When two transactions locked the same number of items Each transaction has a descriptor with a lock Use DCAS to race for locking the two descriptors  Winner calls the shots… 22

35. 35 Wrap-Up Can be shown to guarantee progress in small neighborhoods  If I take many steps, then a transaction within “short distance” completes  The distance depends on size of the data set. Can be made non-blocking / wait-free  By integrating a helping mechanism In a graph on the transactions defined by data conflicts

36. 36 Measuring Concurrency: Spatial Relations between Operations A set of operations induces a conflict graph  Nodes represent items  Edges connect items of the same operation Chains of operations  Paths  Distance is length of path (here, 2)

37. 37 Measuring Concurrency: Spatial Relations between Operations Disjoint access  Non adjacent edges  Distance is infinite Overlapping operations  Adjacent edges  Distance is 0 d-neighborhood of an operation: all operations at distance ≤ d

38. 38 Formally: Interference between Operations Disjoint access Overlapping operations Non-overlapping operations Provides more concurrency & yields better throughput Interference inevitable no interference Should not interfere!

39. 39 A Lot More to be Done Better algorithms for partial snapshots, incorporated into full-fledged STM Other lower bounds (w/ weaker notions of DAP or weaker consistency conditions) More precise definitions of concurrency (& their practical validation) Better and simpler algorithms Definitions of other STM properties (liveness, responsiveness)

40. Thank you!