1. Multicore Programming
Universal & Cache
Tutorial 7
CS Spring 2010

2. Summary
Universal overview
Universal questions
Cache coherency - MESI

3. Theorem: Universality
Consensus is universal
From n-thread consensus build a
Wait-free
Linearizable
n-threaded implementation
Of any sequentially specified object
Art of Multiprocessor Programming 3 3

4. Universal Application Part I
public Response apply(Invoc invoc) {
int i = ThreadID.get();
Node prefer = new node(invoc);
while (prefer.seq == 0) {
Node before = Node.max(head);
Node after =
before.decideNext.decide(prefer);
before.next = after;
after.seq = before.seq + 1;
head[i] = after; } …
Notice that the setting could be by a node other than the one whose method call the winning node represents.
Art of Multiprocessor Programming 4 4

5. Universal Application Part II
...
//compute my response
SeqObject MyObject = new SeqObject();
current = tail.next;
while (current != prefer){
MyObject.apply(current.invoc); current = current.next; }
return MyObject.apply(current.invoc);
To compute my response.
Art of Multiprocessor Programming 5 5

6. Wait-Free Sliding Help Window
while (announce[i].seq == 0) {
Node before = head[i];
Node help = announce[(before.seq + 1 % n)];
if (help.seq == 0)
prefer = help;
else
prefer = announce[i]; …
Art of Multiprocessor Programming 6 6

7. Ptr to cell thread i wants to append
Wait-free Construction
Ptr to cell thread i wants to append …
announce i
tail 1 2 3 4 …
head i
Art of Multiprocessor Programming 7 7

8. Seq The dummy node at the tail of the list is initially set to 1.
Which of the algorithms (wait/lock-free),
would cease to work correctly if the
sequence number of the dummy node was
initially set to 0?

9. Art of Multiprocessor Programming
Universal Object
public class Universal {
private Node[] head;
private Node tail = new Node();
tail.seq = 1;
for (int j=0; j < n; j++){
head[j] = tail }
tail.seq = 0;
Art of Multiprocessor Programming 9 9

10. Seq Solution Doesn't matter for Lock-Free
Won't work for Wait-Free since the announce array is set to the tail.

11. wait-free universal construction
In the wait-free universal construction
If each thread first tries to append
its own node, and then tries to help
the other thread.
Explain whether this alternative
approach works.

12. Nondeterministic Propose a way to fix the universal
construction to work for objects with
nondeterministic sequential
specifications.

13. Nondeterministic solution
Replace with an equivalent deterministic object.
Add another consensus object to each node, publishing the new state.

14. Headless solution Propose a way to avoid using distributed head.
public class Universal {
private Node[] head;
private Node tail = new Node();
tail.seq = 1;
for (int j=0; j < n; j++){
head[j] = tail }

15. Headless solution Replace the call of max() with :
public Node last(Node tail){
Node prev = tail;
Node current = prev.next;
while(true){
if(current==null || current.seq==0)‏
return prev;
prev = current;
current = current.next; }

16. Bounded memory Propose a way to fix the universal
construction to work with bounded of
memory.

17. Bounded memory solution
Add a “Garbage collection”.
Update the tail reference to next node that all the heads passed.

18. Modified, Exclusive, Shared & Invalid
MESI
Modified, Exclusive, Shared & Invalid

19. MESI What is the advantages of distinguishing Exclusive and Modified?
What is the advantages of distinguishing Exclusive and Shared?

20. Art of Multiprocessor Programming
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