Parallel Application Scaling, Performance, and Efficiency

David Skinner

NERSC/LBL

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

Topics

• Application Scaling

• Load Balance

• Synchronization

• Simple stuff

• File I/O

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 balancecomputational goal

vs.compute resources?

Choose the right scale!

Let’s jump to an example

• Sharks and Fish II : N2 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 31 31 32

Sharks and Fish II : Program

Data:

n_fish global

my_fish local

fishi = {x, y, …}

Dynamics:

F = ma

…

V = Σ 1/rij

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 ai += g * massj * ( fishi – fishj ) / rij

}}

Move fish

• 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

Scaling: Good 1st Step: Do runtimes make sense?

1 Task

32 Tasks

…

Running fish_sim for 100-1000 fish on 1-32 CPUs we see

time ~ fish2

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

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 = Ts/Tp(n)

–Efficiency = Ts/(n*Tp(n))

Multiple definitions

exist!

Scaling: Speedups

Scaling: Efficiencies

Remarkably smooth! Often algorithm and architecture make efficiency landscape quite complex

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

W

hoa!

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

Scaling: Superlinear Speedup

# CPUs(OMP)

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 decreasing2) Synchronization rate is increasing3) Surface:Volume ratio is increasing

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 EwaldMatSci Computation

600s@256 way or

80s@1024 way

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

Load Balance : Application Cartoon

Universal App Unbalanced:

Balanced:

Time saved by load balanceWill define synchronization later

Load Balance : performance data

MPI ranks sorted by total communication time

Communication Time: 64 tasks show 200s, 960 tasks show 230s

Load Balance: ~code

while(1) {

do_flops(Ni);

MPI_Alltoall();

MPI_Allreduce();

}

960 x

64x

Load Balance: real code

Sync

Flops

Exchange

Time

MP

I Ra

nk

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!

Load Balance : FFT

Q: When is imbalance good? A: When is leads to a faster Algorithm.

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

Topics

• Load Balance

• Synchronization

• Simple stuff

• File I/O

Scaling of MPI_Barrier()

fourorders of magnitude

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?

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

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…

Colony Switch

Colony Switch

PG F S

seaborg.nersc.gov basics

Resource Speed Bytes

Registers 3 ns 2560 B

L1 Cache 5 ns 32 KB

L2 Cache 45 ns 8 MB

Main Memory 300 ns 16 GB

Remote Memory 19 us 7 TB

GPFS 10 ms 50 TB

HPSS 5 s 9 PB

380 x

HPSSHPSS

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 MemoryGPFS

IBM SP

Colony Switch

Colony Switch

PG F S

MPI on the IBM SP

HPSSHPSS

CSS0

CSS1

16 way SMP NHII Node

Main MemoryGPFS

•2-4096 way concurrency

•MPI-1 and ~MPI-2

•GPFS aware MPI-IO

•Thread safety

•Ranks on same node bypass the switch

MPI: seaborg.nersc.gov

Intra and Inter Node Communication

MP_EUIDEVICE

(fabric)

Bandwidth

(MB/sec)

Latency

(usec)

css0 500 / 350 9 / 21

css1 X X

csss 500 / 350 9 / 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 MemoryGPFS

css0

css1

csss

Seaborg : point to point messaging

16 way SMP NHII Node

Main MemoryGPFS

16 way SMP NHII Node

Main MemoryGPFS

IntranodeInternode

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.

Inter-Node Bandwidth

csss

css0

• Tune message size to optimize throughput

• Aggregate messages when possible

MPI Performance is often Hierarchical

message size and task placement are key to performance

Intra

Inter

MPI: Latency not always 1 or 2 numbers

The set of all possibly latencies describes

the interconnect geometry from the application

perspective

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 …

Synchronization: MPI Collectives

2048 tasks

Beyond load balance there is a distribution on MPI timings intrinsic to the MPI Call

Synchronization: Architecture

t is the frequencykernel process

scheduling

Unix : cron et al.

…and from the machine itself

Intrinsic Synchronization : Alltoall

Intrinsic Synchronization: Alltoall

Architecture makes a big difference!

This leads to variability in Execution Time

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

Topics

• Load Balance

• Synchronization

• Simple stuff

• File I/O

Simple Stuff

Parallel programs are easier to mess up than serial ones. Here are some common

pitfalls.

What’s wrong here?

Is MPI_Barrier time bad? Probably. Is it avoidable?

~three cases:1) The stray / unknown / debug barrier2) The barrier which is masking compute balance 3) Barriers used for I/O ordering

Often very easy to fix

MPI_Barrier

Topics

• Load Balance

• Synchronization

• Simple stuff

• File I/O

Parallel File I/O : Strategies

MPI

Disk

Some strategies fall down at scale

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

Topics

• Load Balance

• Synchronization

• Simple stuff

• File I/O

Happy Scaling!

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

Dynamical Load Balance: Motivation

Time

MPI R

an

k

Sync

Flops

Exchange