HPC Benchmarks Profiling HPGMG Bof · ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ Memory/Compute bound – Byte/FLOP 1/2 benchmark kernel

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HPC Benchmarking

Vladimir Marjanovic, Colin W. Glass, Jose Gracia

18.11.2015:: :: ::V.Marjanovic HPGMG BoF

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�� Goals of TOP500 HPC Benchmarking

• Ranking supercomputers

• One number all properties

18.11.2015:: :: ::V.Marjanovic HPGMG BoF 2

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�� HPC Benchmarking Approaches

• Two approaches:

– single application (kernel) :

HPL, HPCG, HPGMG

– many applications (kernels):

HPGMG, NAS benchmark, HPC Challenge, MPI SPEC 2007 etc


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�� Real App Representation

• HPL ‐ direct solver O(n3)

• HPCG, HPGMG(FV, FE) – iterative solver O(n)

• HPL is n2 times slower than HPCG and HPGMG


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�� HPC Reference Codes

MPI OpenMP External lib Metric

HPL yes BLAS MT BLAS GFLOP/s

HPCG yes SpMV no GFLOP/s

HPGMG‐FV yes yes no DoF/s

HPGMG‐FE yes no PETSC GFLOP/s

• Well written balanced codes• HPCG – MG only 3 levels• HPGMG – MG many levels

Level 1

level 2


Level 1

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�� Important System Properties

• Compute power (Flop/s)

• Main Memory BW (B/s)

Nodes

………..

• IC BW(B/s)

• IC latency(s)

• IC message rate Network

………..

One number = f(properties)


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�� Memory/Compute bound – Byte/FLOP 1/2

memorybenchmark kernel Byte/FLOP

HPL DGEMM 12/n = f(n)

HPCG SpMV, SYMGS > 4memory BW

cache

p ,

HPGMG GSRB >1

• Modern hardware ≈ 0.3 Byte/Flop

coree.g E2680v3 has 0.14 Byte/Flop

NEC SX‐ACE 1Byte/Flop

• HPCG & HPGMG kernels are memory bound on modern hardware


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�� Memory/Compute bound – Byte/FLOP 2/2


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�� HPL, HPCG, HPGMG core&node

HPCG:

Gflops 2.75x

BW 2 63xBW 2.63x

HPGMG:

Gflops 4.78x

BW 4 77BW 4.77x

HPL

~8x


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�� HPCG Intel Optimized Version


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�� HPGMG‐FV NEC‐ACE versus CRAY XC30

Ivy Bridge 5576

NEC SX‐ACE

• 4 cores for 256GFlops4 cores for 256GFlops peak performance

• 1 GHz

• 16 vectore pipes per core• 16 vectore pipes per core

• 32 memory channels for 256GB/s bandwidth, one core or sharablecore or sharable


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�� Communication HPL

• MPI communicators

• whole range of message sizes

(few bytes < size < 100 MB)(few bytes < size < 100 MB)

• large number of small messages

(fact > 256)

stresses bandwidth, latency and message rate


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�� Communication HPCG

• small and large messages

(few bytes < size < 512 KB (4 MB))(few bytes < size < 512 KB (4 MB))

• number of messages

(ex.halos max is 26)

stresses latency


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�� Communication HPGMG‐FV


• small and medium messages few (bytes < size < 4 MB)(bytes < size < 4 MB)


(> 800 for mpi64)n3

stresses latency and message rate


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�� Communication HPGMG‐FE


• small and medium messages few (bytes < size < 4 MB)(bytes < size < 4 MB)


stresses latency and message rate


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�� HPL HPCG HPGMG Overview

Representation

ComputePower

Memory BW

IC BW

ICLatency

ICRouting

HPL X X

HPCG X X X

HPGMG X

• Potential of overlapping of communication and computation

• What will happened in poor IC ( Data Center, Cloud) ?


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�� Arbitrary problem size issue• HPL complexity: computational O(n3) communication O(n2)

l i i l ( ) i i ( 2/3)• HPCG,HPGMG complexity: computational O(n) communication O(n2/3)

• Large problem size ‐> computation dominates communicationLarge problem size > computation dominates communication

• Uniform behavior of routines or single dominant routine

• HPL ‐ > DGEMM

• HPCG ‐ > SpMV, SYMGS

• HPGMG ‐> GSRB


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�� Conclusions

• Stresses memory bandwidth, compute unit and routing

• Representation of real applications

• Arbitrary problem size (weighting or integral as solution)

• Clear rules for benchmarking


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HPC Benchmarks Profiling HPGMG Bof · ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ ˜˜˜˜˜ Memory/Compute bound – Byte/FLOP 1/2 benchmark kernel

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