1. Parallel Application Scaling, Performance, and Efficiency David Skinner NERSC/LBL

2. Parallel Scaling of MPI Codes A practical talk on using MPI with focus on: Distribution of work within a parallel program Placement of computation within a parallel computer Performance costs of various types of communication Understanding scaling performance terminology

3. Topics Application Scaling Load Balance Synchronization Simple stuff File I/O

4. Let’s jump to an example Sharks and Fish II : N 2 force summation in parallel E.g. 4 CPUs evaluate force for 125 fish Domain decomposition: Each CPU is “in charge” of ~31 fish, but keeps a fairly recent copy of all the fishes positions (replicated data) Is it not possible to uniformly decompose problems in general, especially in many dimensions Luckily this problem has fine granularity and 2D, let’s see how it scales 31 32

5. Sharks and Fish II : Program Data: n_fish  global my_fish  local fish i = {x, y, …} Dynamics: F = ma … V = Σ 1/r ij qdot = dH/dp pdot = -dV/dq MPI_Allgatherv(myfish_buf, len[rank], MPI_FishType…) for (i = 0; i < my_fish; ++i) { for (j = 0; j < n_fish; ++j) { // i!=j a i += g * mass j * ( fish i – fish j ) / r ij } Move fish

6. 100 fish can move 1000 steps in 1 task  5.459s 32 tasks  2.756s 1000 fish can move 1000 steps in 1 task  511.14s 32 tasks  20.815s What’s the “best” way to run? –How many fish do we really have? –How large a computer (time) do we have? –How quickly do we need the answer? Sharks and Fish II: How fast? x 24.6 speedup x 1.98 speedup

7. Scaling: Good 1 st Step: Do runtimes make sense? 1 Task 32 Tasks … Running fish_sim for 100-1000 fish on 1-32 CPUs we see

8. Scaling: Walltimes Walltime is (all)important but let’s define some other scaling metrics

9. Scaling: definitions Scaling studies involve changing the degree of parallelism. Will we be change the problem also? Strong scaling –Fixed problem size Weak scaling – Problem size grows with additional resources Speed up = T s /T p (n) Efficiency = T s /(n*T p (n)) Multiple definitions exist!

10. Scaling: Speedups

11. Scaling: Efficiencies Remarkably smooth! Often algorithm and architecture make efficiency landscape quite complex

12. Scaling: Analysis Why does efficiency drop? –Serial code sections  Amdahl’s law –Surface to Volume  Communication bound –Algorithm complexity or switching –Communication protocol switching  Whoa!

13. Scaling: Analysis In general, changing problem size and concurrency expose or remove compute resources. Bottlenecks shift. In general, first bottleneck wins. Scaling brings additional resources too. –More CPUs (of course) –More cache(s) –More memory BW in some cases

14. Scaling: Superlinear Speedup # CPUs (OMP)

15. Scaling: Communication Bound 64 tasks, 52% comm 192 tasks, 66% comm 768 tasks, 79% comm MPI_Allreduce buffer size is 32 bytes. Q: What resource is being depleted here? A: Small message latency 1)Compute per task is decreasing 2)Synchronization rate is increasing 3)Surface : Volume ratio is increasing

16. Topics Load Balance Synchronization Simple stuff File I/O

17. Load Balance : cartoon Universal App Unbalanced: Balanced: Time saved by load balance

18. Load Balance : performance data MPI ranks sorted by total communication time Communication Time: 64 tasks show 200s, 960 tasks show 230s

19. Load Balance: ~code while(1) { do_flops(N i ); MPI_Alltoall(); MPI_Allreduce(); } 960 x 64 x

20. Load Balance: real code Sync Flops Exchange Time  MPI Rank 

21. Load Balance : analysis The 64 slow tasks (with more compute work) cause 30 seconds more “communication” in 960 tasks This leads to 28800 CPU*seconds (8 CPU*hours) of unproductive computing All imbalance requires is one slow task and a synchronizing collective! Pair well problem size and concurrency. Parallel computers allow you to waste time faster!

22. Load Balance : FFT Q: When is imbalance good? A: When is leads to a faster Algorithm.

23. Load Balance: Summary Imbalance most often a byproduct of data decomposition Must be addressed before further MPI tuning can happen Good software exists for graph partitioning / remeshing For regular grids consider padding or contracting

24. Topics Load Balance Synchronization Simple stuff File I/O

25. Scaling of MPI_Barrier() four orders of magnitude

26. Synchronization: definition MPI_Barrier(MPI_COMM_WORLD); T1 = MPI_Wtime(); e.g. MPI_Allreduce(); T2 = MPI_Wtime()-T1; For a code running on N tasks what is the distribution of the T2’s? The average and width of this distribution tell us how synchronizing e.g. MPI_Allreduce is Completions semantics of MPI functions 1)Local : leave based on local logic (MPI_Comm_rank) 2)Partially synchronizing : leave after messaging M<N tasks (MPI_Bcast, MPI_Reduce) 3)Fully synchronizing : leave after every else enters (MPI_Barrier, MPI_Allreduce) How synchronizing is MPI_Allreduce?

27. seaborg.nersc.gov It’s very hard to discuss synchronization outside of the context a particular parallel computer So we will examine parallel application scaling on an IBM SP which is largely applicable to other clusters

28. Colony Switch PGFS seaborg.nersc.gov basics ResourceSpeedBytes Registers 3 ns2560 B L1 Cache 5 ns 32 KB L2 Cache 45 ns 8 MB Main Memory300 ns 16 GB Remote Memory 19 us 7 TB GPFS 10 ms 50 TB HPSS 5 s 9 PB 380 x HPS S CSS0 CSS1 6080 dedicated CPUs, 96 shared login CPUs Hierarchy of caching, speeds not balanced Bottleneck determined by first depleted resource 16 way SMP NHII Node Main Memory GPFS IBM SP

29. Colony Switch PGFS MPI on the IBM SP HPS S CSS0 CSS1 16 way SMP NHII Node Main Memory GPFS 2-4096 way concurrency MPI-1 and ~MPI-2 GPFS aware MPI-IO Thread safety Ranks on same node bypass the switch

30. MPI: seaborg.nersc.gov Intra and Inter Node Communication MP_EUIDEVICE (fabric) Bandwidth (MB/sec) Latency (usec) css0500 / 3509 / 21 css1XX csss500 / 3509 / 21 Lower latency  can satisfy more syncs/sec What is the benefit of two adapters? This is for a single pair of tasks 16 way SMP NHII Node Main Memory GPFS css0 css1 csss

31. Seaborg : point to point messaging 16 way SMP NHII Node Main Memory GPFS 16 way SMP NHII Node Main Memory GPFS Intranode Internode Switch bandwidth is often stated in optimistic terms

32. Inter-Node Bandwidth  csss css0  Tune message size to optimize throughput Aggregate messages when possible

33. MPI Performance is often Hierarchical message size and task placement are key Intra Inter

34. MPI: Latency not always 1 or 2 numbers The set of all possibly latencies describes the interconnect from the application perspective

35. Synchronization: measurement MPI_Barrier(MPI_COMM_WORLD); T1 = MPI_Wtime(); e.g. MPI_Allreduce(); T2 = MPI_Wtime()-T1; How synchronizing is MPI_Allreduce? For a code running on N tasks what is the distribution of the T2’s? Let’s measure this…

36. Synchronization: MPI Collectives 2048 tasks Beyond load balance there is a distribution on MPI timings intrinsic to the MPI Call

37. Synchronization: Architecture t is the frequency kernel process scheduling Unix : cron et al. …and from the machine itself

38. Intrinsic Synchronization : Alltoall

39. Architecture makes a big difference!

40. This leads to variability in Execution Time

41. Synchronization : Summary As a programmer you can control –Which MPI calls you use (it’s not required to use them all). –Message sizes, Problem size (maybe) –The temporal granularity of synchronization Language Writers and System Architects control –How hard is it to do last two above –The intrinsic amount of noise in the machine

42. Topics Load Balance Synchronization Simple stuff File I/O

43. Simple Stuff Parallel programs are easier to mess up than serial ones. Here are some common pitfalls.

44. What’s wrong here?

45. Is MPI_Barrier time bad? Probably. Is it avoidable? ~three cases: 1)The stray / unknown / debug barrier 2)The barrier which is masking compute balance 3)Barriers used for I/O ordering Often very easy to fix MPI_Barrier

46. Topics Load Balance Synchronization Simple stuff File I/O

47. Parallel File I/O : Strategies MPI Disk Some strategies fall down at scale

48. Parallel File I/O: Metadata A parallel file system is great, but it is also another place to create contention. Avoid uneeded disk I/O, know your file system Often avoid file per task I/O strategies when running at scale

49. Topics Load Balance Synchronization Simple stuff File I/O Happy Scaling!

50. Other sources of information: MPI Performance: http://www-unix.mcs.anl.gov/mpi/tutorial/perf/mpiperf/ Seaborg MPI Scaling: http://www.nersc.gov/news/reports/technical/seaborg_scaling/ MPI Synchronization : Fabrizio Petrini, Darren J. Kerbyson, Scott Pakin, "The Case of the Missing Supercomputer Performance: Achieving Optimal Performance on the 8,192 Processors of ASCI Q", in Proc. SuperComputing, Phoenix, November 2003. Domain decomposition: http://www.ddm.org/ google://”space filling”&”decomposition” etc. Metis : http://www-users.cs.umn.edu/~karypis/metis

51. Dynamical Load Balance: Motivation Time  MPI Rank  Sync Flops Exchange