1. מרצה: יהודה אפק מגיש: ערן שרגיאן

2. OutlineOutline Quick reminder of the Stack structure. The Unbounded Lock-Free Stack. The Elimination Backoff Stack.

3. Concurrent Stack The Stack class is a collection of items (of type T) that provides the following methods: push(x) pop() Satisfying the Last-In-First-Out (LIFO) property: The last item pushed is the first popped.

4. Empty Stack Top

5. PushPush

6. PushPush CAS

7. PushPush Top

8. PushPush

9. PushPush

10. PushPush CAS

11. PushPush Top

12. PopPop

13. PopPop CAS

14. PopPop Top CAS mine!

15. PopPop Top CAS

16. PopPop Top

17. The LockfreeStack class The lock-free stack is a linked list, where the top field points to the first node (or null if the stack is empty). A pop() call uses compareAndSet() to try to remove the first node from the stack. A push() call uses compareAndSet() to try to insert a new node into the top of the stack.

18. public class LockFreeStack { private AtomicReference top = new AtomicReference(null); static final int MIN_DELAY = …; static final int MAX_DELAY = …; Backoff backoff = new Backoff(MIN_DELAY, MAX_DELAY); public boolean tryPush(Node node){ Node oldTop = top.get(); node.next = oldTop; return(top.compareAndSet(oldTop, node)) } public void push(T value) { Node node = new Node(value); while (true) { if (tryPush(node)) { return; } else backoff.backoff(); }

19. public boolean tryPop() throws EmptyException { Node oldTop = top.get(); if (oldTop == null) { throw new EmptyException(); } Node newTop = oldTop.next; if (top.compareAndSet(oldTop, newTop)) { return oldTop; } else { return null; } public T pop() throws EmptyException { while (true) { Node returnNode = tryPop(); if (returnNode != null) { return returnNode.value; } else backoff.backoff(); }

20. Lock-free Stack Good No locking Bad huge contention at top No parallelism

21. Elimination-Backoff Stack Ways to solve it : exponential backoff (reduces contention but does not solve the bottleneck problem). elimination backoff The LockFreeStack implementation scales poorly, not so much because the stack’s top field is a source of contention, but primarily because it is a sequential bottleneck.

22. ObservationObservation Push( ) Pop() linearizable stack After an equal number of pushes and pops, stack stays the same Yes!

23. Idea: Elimination Array Push( ) Pop() stack Pick at random Pick at random Elimination Array

24. Push Collides With Pop Push( ) Pop() stack continue No need to access stack Yes!

25. No Collision Push( ) Pop() stack If no collision, access stack If pushes collide or pops collide access stack

26. Elimination-Backoff Stack A union of the LockFreeStack class with the elimination array Access Lock-free stack, If uncontended, apply operation if contended, back off to elimination array and attempt elimination

27. Elimination-Backoff Stack Push( ) Pop() Top CAS If CAS fails, back off

28. Dynamic Range and Delay Push( ) Pick random range and max time to wait for collision based on level of contention encountered

29. LinearizabilityLinearizability The combined data structure, array, and shared stack, is linearizable because the shared stack is linearizable, and the eliminated calls can be ordered as if they happened at the point in which they exchanged values. Un-eliminated calls linearized as before Eliminated calls: linearize pop() immediately after matching push() Combination is a linearizable stack

30. Un-Eliminated Linearizability push(v 1 ) time linearizable push(v 1 ) pop(v 1 )

31. Eliminated Linearizability pop(v 2 )push(v 1 ) push(v 2 ) time push(v 2 ) linearizable pop(v 2 ) push(v 1 ) pop(v 1 ) Collision Point Red calls are eliminated

32. Backoff Has Dual Effect Elimination introduces parallelism Backoff onto array cuts contention on lock-free stack Elimination in array cuts down total number of threads ever accessing lock-free stack

33. public class EliminationArray { private static final int duration =...; private static final int timeUnit =...; Exchanger [] exchanger; public EliminationArray(int capacity) { exchanger = new Exchanger[capacity]; for (int i = 0; i < capacity; i++) exchanger[i] = new Exchanger (); … } … } Elimination Array

34. public class Exchanger { AtomicStampedReference slot = new AtomicStampedReference (null, 0); A Lock-Free Exchanger

35. Atomic Stamped Reference addressS Stamp Reference

36. Exchanger Status enum Status {EMPTY, WAITING, BUSY};

37. Lock-free Exchanger EMPTY

38. Lock-free Exchanger CAS

39. WAITING Lock-free Exchanger

40. In search of partner … WAITING

41. Lock-free Exchanger Slot Still waiting … Try to exchange item and set state to BUSY CAS

42. BUSY Lock-free Exchanger Slot Partner showed up, take item and reset to EMPTY item stamp/state

43. EMPTYBUSY Lock-free Exchanger Slot item stamp/state Partner showed up, take item and reset to EMPTY

44. The Exchanger Slot Exchanger is lock-free Because the only way an exchange can fail is if others repeatedly succeeded or no-one showed up

45. public class EliminationArray { … public T visit(T value, int Range) throws TimeoutException { int slot = random.nextInt(Range); int nanodur = convertToNanos(duration, timeUnit)); return (exchanger[slot].exchange(value, nanodur) }} Elimination Array

46. public void push(T value) {... while (true) { if (tryPush(node)) { return; } else try { T otherValue = eliminationArray.visit(value,policy.Range); if (otherValue == null) { return; } Elimination Stack Push

47. public T pop() {... while (true) { if (tryPop()) { return returnNode.value; } else try { T otherValue = eliminationArray.visit(null,policy.Range); if (otherValue != null) { return otherValue; } }} Elimination Stack Pop

48. SummarySummary Quick reminder of the Stack structure. The Unbounded Lock-Free Stack. The Elimination Backoff Stack.

49. תודה רבה על ההקשבה