Presentation is loading. Please wait.

Presentation is loading. Please wait.

Local-Spin Algorithms Multiprocessor synchronization algorithms (20225241) Lecturer: Danny Hendler This presentation is based on the book “Synchronization.

Similar presentations


Presentation on theme: "Local-Spin Algorithms Multiprocessor synchronization algorithms (20225241) Lecturer: Danny Hendler This presentation is based on the book “Synchronization."— Presentation transcript:

1 Local-Spin Algorithms Multiprocessor synchronization algorithms (20225241) Lecturer: Danny Hendler This presentation is based on the book “Synchronization Algorithms and Concurrent Programming” by G. Taubenfeld and on a the survey “Shared-memory mutual exclusion: major research trends since 1986” by J. Anderson, Y-J. Kim and T. Herman

2 Remote and local memory accesses In a DSM system: local remote In a Cache-coherent system: An access of v by p is remote if it is the first access of v or if v has been written by another process since p’s last access of it.

3 Local-spin algorithms In a local-spin algorithm, all busy waiting (‘await’) is done by read-only loops of local-accesses, that do not cause interconnect traffic. The same algorithm may be local-spin on one architecture (DSM or CC) and non-local spin on the other. For local-spin algorithms, our complexity metric is the worst-case number of Remote Memory References (RMRs)

4 Peterson’s 2-process algorithm Program for process 1 1.b[1]:=true 2.turn:=1 3.await (b[0]=false or turn=0) 4.CS 5.b[1]:=false Program for process 0 1.b[0]:=true 2.turn:=0 3.await (b[1]=false or turn=1) 4.CS 5.b[1]:=false Is this algorithm local-spin on a DSM machine? No Is this algorithm local-spin on a CC machine? Yes

5 Recall the following simple test-and-set based algorithm Shared lock initially 0 1.While (! lock.test-and-set() ) // entry section 2.Critical Section 3.Lock := 0 // exit section This algorithm is not local-spin on neither a DSM or CC machine (A RMW operation always incurs an RMR)

6 A better algorithm: test-and-test-and-set Shared lock initially 0 1.While (! lock.test-and-set() )// entry section 2. await(lock == 0) 3.Critical Section 4.Lock := 0 // exit section Creates less traffic in CC machines, still not local-spin.

7 Local Spinning Mutual Exclusion Using Strong Primitives

8 Anderson’s queue-based algorithm (Anderson, 1990) Shared: integer ticket – A RMW object, initially 0 bit valid[0..n-1], initially valid[0]=1 and valid[i]=0, for i  {1,..,n-1} Local: integer myTicket Program for process i 1.myTicket=fetch-and-inc-modulo-n(ticket) ; take a ticket 2.await valid[myTicket]=1 ; wait for your turn 3.CS 4.valid[myTicket]:=0 ; dequeue 5.valid[myTicket+1 mod n]:=1 ; signal successor 0123n-1 valid10 1 0000 ticket

9 Anderson’s queue-based algorithm (cont’d) 0 ticket valid 10000 Initial configuration 1 ticket valid 10000 After entry section of p 3 0 myTicket 3 After p 1 performs entry section 2 ticket valid 10000 0 myTicket 3 1 myTicket 1 2 ticket valid 01000 After p 3 exits 1 myTicket 1

10 Anderson’s queue-based algorithm (cont’d) What is the RMR complexity on a DSM machine? Unbounded What is the RMR complexity on a CC machine? Constant Program for process i 1.myTicket=fetch-and-inc-modulo-n(ticket) ; take a ticket 2.await valid[myTicket]=1 ; wait for your turn 3.CS 4.valid[myTicket]:=0 ; dequeue 5.valid[myTicket+1 mod n]:=1 ; signal successor

11 The MCS queue-based algorithm (Mellor-Crummey and Scott, 1991) Type: Qnode: structure {bit locked, Qnode *next} Shared: Qnode nodes[0..n-1] Qnode *tail initially null Local: Qnode *myNode, initially &nodes[i] Qnode *successor Has constant RMR complexity under both the DSM and CC models Uses swap and CAS Tail nodes 1 2 3 n-1 n FTT

12 The MCS queue-based algorithm (cont’d) Program for process i 1.myNode->next := null; prepare to be last in queue 2.pred=swap(&tail, myNode ) ;tail now points to myNode 3.if (pred ≠ null) ;I need to wait for a predecessor 4. myNode->locked := true ;prepare to wait 5. pred->next := myNode ;let my predecessor know it has to unlock me 6. await myNode.locked := false 7.CS 8.if (myNode.next = null) ; if not sure there is a successor 9. if (compare-and-swap(&tail, myNode, null) = false) ; if there is a successor 10. await (myNode->next ≠ null) ; spin until successor lets me know its identity 11. successor := myNode->next ; get a pointer to my successor 12. successor->locked := false ; unlock my successor 13.else ; for sure, I have a successor 14. successor := myNode->next ; get a pointer to my successor 15. successor->locked := false ; unlock my successor

13 The MCS queue-based algorithm (cont’d)

14 Local Spinning Mutual Exclusion Using reads and writes

15 A local-spin tournament-tree algorithm (Anderson, Yang, 1993) O(log n) RMR complexity for both DSM and CC systems This is optimal (Attiya, Hendler, woelfel, 2008) Uses O(n log n) registers 0 0 1 0 1 2 3 0 1 2 3 4 5 6 7 Level 0 Level 1 Level 2 Processes Each node is identified by (level, number)

16 A local-spin tournament-tree algorithm (cont’d) Shared: - Per each node, v, there are 3 registers: name[level, 2node], name[level, 2node+1] initially -1 turn[level, node] - Per each level l and process i, a spin flag: flag[ level, i ] initially 0 Local : level, node, id

17 A local-spin tournament-tree algorithm (cont’d) Program for process i 1.node:=i 2.For level = o to log n-1 do ;from leaf to root 3. node:=  node/2  ;compute node in new level 4. id=node mod 2 ; compute ID for 2-process mutex algorithm (0 or 1) 5. name[level, 2node + id]:=i ;identify yourself 6. turn[level,node]:=i ;update the tie-breaker 7. flag[level, i]:=0 ;initialize my locally-accessible spin flag 8. rival:=name[level, 2node+1-id] 9. if ( (rival ≠ -1) and (turn[level, node] = i) ) ;if not sure I should precede rival 10. if (flag[level, rival] =0) If rival may get to wait at line 14 11. flag[level, rival]:=1 ;Release rival by letting it know I updated tie-breaker 12. await flag[level, i] ≠ 0 ;await until signaled by rival (so it updated tie-breaker) 13. if (turn[level,node]=i) ;if I lost 14. await flag[level,i]=2 ;wait till rival notifies me its my turn 15. id:=node ;move to the next level 16.EndFor 17.CS 18.for level=log n –1 downto 0 do ;begin exit code 19. id:=  i/2 level, node:=  id/2  ;set node and id 20. name[level, 2node+id ]) :=-1 ;erase name 21. rival := turn[level,node] ;find who rival is (if there is one) 22. if rival ≠ i ;if there is a rival 23. flag[level,rival] :=2 ;notify rival

18 Local-Spin Leader Election Exactly one process is elected All other processes are not-elected Processes may busy-wait

19 Choy and Sing's filter Filter m processes The rest are “halted” Between 1 and  m/2  processes “exit “ Filter guarantees: Safety: if m processes enter a filter, at most  m/2  exit. Progress: if some processes enter a filter, at least one exits.

20 Choy and Singh's filter (cont’d) Shared: integer turn Boolean b, initially false Program for process i 1.turn := i 2.await  b // wait for barrier to open 3.b := true // close barrier 4.if turn ≠ i // not last to cross the barrier 5. b := false // open barrier 6. halt 7.else 8. exit Why are filter guarantees satisfied? Why does the barrier has to be re-opened?

21 Choy and Sing’s filter algorithm Filter #1 Filter #2 Filter #i

22 Choy and Sing’s filter algorithm (cont’d) Shared: typdef struct{integer turn, boolean b,c initially false} filter filter A[log n + 1] Program for process i 1.For (curr=0; cur < log n +1; curr++) 2. A[curr].turn := p 3. Await  A[curr].b 4. A[curr].b:=true 5. if (A[curr]. turn ≠ i) 6. A[curr].c := true // mark that some process failed on filter 7. A[curr].b := false 8. return not-elected 9. else if (curr > 0)   A[curr-1].c 10. return elected // Other processes will never exit this filter 11. else 12. curr := curr+1 13.EndFor Do you see any problem with this algorithm? How can this be fixed?

23 Choy and Sing’s filter algorithm (cont’d) What is the DSM RMR complexity? Unbounded Program for process i 1.For (curr=0; cur < log n +1; curr++) 2. A[curr].turn := p 3. Await  A[curr].b 4. A[curr].b:=true 5. if (A[curr]. turn ≠ i) 6. A[curr].c := true // mark that some process failed on filter 7. A[curr].b := false 8. return not-elected 9. else if (curr > 0)   A[curr-1].c 10. return elected // Other processes will never reach this filter 11. Else 12. curr := curr+1 13.EndFor

24 Choy and Sing’s filter algorithm (cont’d) What is the CC RMR complexity? Program for process i 1.For (curr=0; cur < log n +1; curr++) 2. A[curr].turn := p 3. Await  A[curr].b 4. A[curr].b:=true 5. if (A[curr]. turn ≠ i) 6. A[curr].c := true // mark that some process failed on filter 7. A[curr].b := false 8. return not-elected 9. else if (curr > 0)   A[curr-1].c 10. return elected // Other processes will never reach this filter 11. Else 12. curr := curr+1 13.EndFor

25 Choy and Sing’s filter algorithm (cont’d) What is the CC RMR complexity? Program for process i 1.For (curr=0; cur < log n +1; curr++) 2. A[curr].turn := p 3. Await  A[curr].b 4. A[curr].b:=true 5. if (A[curr]. turn ≠ i) 6. A[curr].c := true // mark that some process failed on filter 7. A[curr].b := false 8. return not-elected 9. else if (curr > 0)   A[curr-1].c 10. return elected // Other processes will never reach this filter 11. Else 12. curr := curr+1 13.EndFor A process may incur here a linear number of RMRs

26 What is the worst-case CC RMR complexity? Choy and Sing’s filter algorithm (cont’d) Linear Any ideas for a (log n)-RMRs algorithm? A simple modification of the tournament-tree algorithm

27 Is there an O(1) RMRs leader election algorithm from reads and writes? Yes [Golab, Hendler and Woelfel, 2006] Conditional primitives (e.g. compare-and-swap) are no stronger than reads & writes for RMR complexity [Golab, Hadzilacos, Hendler and Woelfel, 2007]


Download ppt "Local-Spin Algorithms Multiprocessor synchronization algorithms (20225241) Lecturer: Danny Hendler This presentation is based on the book “Synchronization."

Similar presentations


Ads by Google