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 different types of communication Understanding scaling performance terminology

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

4. Scale: Practical Importance Time required to compute the NxN matrix product C=A*B Assuming you can address 64GB from one task, can you wait a month? How to balance computational goal vs. compute resources? Choose the right scale!

5. Let’s jump to an example Sharks and Fish II : N 2 parallel force evalulation 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 This toy problem is simple, has fine granularity and is 2D Let’s see how it scales 31 32

6. Sharks and Fish II : Program Data: n_fish  global my_fish  local fish i = {x, y, …} Dynamics: F = ma … V = Σ 1/r ij dq/dt = m * p dp/dt = -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

7. 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 So 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

8. 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 time ~ fish 2

9. Scaling: Walltimes walltime is (all)important but let’s look at some other scaling metrics Each line is contour describing computations doable in a given time

10. Scaling: terminology Scaling studies involve changing the degree of parallelism. Will we be changing the problem also? –Strong scaling  Fixed problem size –Weak scaling  Problem size grows with additional compute resources How do we measure success in parallel scaling? –Speed up = T s /T p (n) –Efficiency = T s /(n*T p (n)) Multiple definitions exist!

11. Scaling: Speedups

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

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

14. 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

15. Scaling: Superlinear Speedup # CPUs (OMP)

16. Strong 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

17. Sharks and Atoms: At HPC centers like NERSC fish are rarely modeled as point masses. The associated algorithms and their scalings are none the less of great practical importance for scientific problems. Particle Mesh Ewald MatSci Computation 600s@256 way or 80s@1024 way

18. Topics Load Balance Synchronization Simple stuff File I/O Now instead of looking at scaling of specific applications lets look at general issues in parallel application scalability

19. Load Balance : Application Cartoon Universal App Unbalanced: Balanced: Time saved by load balance Will define synchronization later

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

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

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

23. 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 load imbalance requires is one slow task and a synchronizing collective! Pair well problem size and concurrency. Parallel computers allow you to waste time faster!

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

25. Load Balance: Summary Imbalance is 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

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

27. Scaling of MPI_Barrier() four orders of magnitude

28. Synchronization: terminology 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 relative to some given interconnect. (HW & SW) How synchronizing is MPI_Allreduce?

29. Synchronization : MPI Functions Completion semantics of MPI functions Local : leave based on local logic –MPI_Comm_rank, MPI_Get_count Probably Local : try to leave w/o messaging other tasks –MPI_Isend/Irecv Partially synchronizing : leave after messaging M<N tasks –MPI_Bcast, MPI_Reduce Fully synchronizing : leave after every else enters –MPI_Barrier, MPI_Allreduce

30. seaborg.nersc.gov It’s hard to discuss synchronization outside of the context a particular parallel computer MPI timings depend on HW, SW, and environment –How much of MPI is handled by the switch adapter? –How big are messaging buffers? –How many thread locks per function? –How noisy is the machine (today)? This is hard to model, so take an empirical approach based on an IBM SP which is largely applicable to other clusters…

31. 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

32. 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

33. 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

34. Seaborg : point to point messaging 16 way SMP NHII Node Main Memory GPFS 16 way SMP NHII Node Main Memory GPFS Intranode Internode Switch BW and latency are often stated in optimistic terms. The number and size of concurrent messages changes things. A fat tree / crossbar switch helps hide this.

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

36. MPI Performance is often Hierarchical message size and task placement are key to performance Intra Inter

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

38. 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? One can derive the level of synchronization from MPI algorithms. Instead let’s just measure …

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

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

41. Intrinsic Synchronization : Alltoall

42. Architecture makes a big difference!

43. This leads to variability in Execution Time

44. 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, i.e., where do synchronization occur. Language writers and system architects control –How hard is it to do the above –The intrinsic amount of noise in the machine

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

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

47. What’s wrong here?

48. 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

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

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

51. 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

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

53. 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

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