hpcg @ arm · inspiration •we have used different sources as inspiration •j. park et al. 2014....
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© 2018 Arm Limited
• Daniel Ruiz• 13th November 2018
HPCG @ Arm
2 © 2018 Arm Limited
Motivation
• HPCG is becoming increasingly important in the HPC world
• Few optimized versions are open-source• None are Arm-specific
• Establish a baseline codebase for the community to build upon
• Stop reinventing the wheel
3 © 2018 Arm Limited
Inspiration
• We have used different sources as inspiration• J. Park et al. 2014. Efficient shared-memory implementation of high-performance conjugate gradient benchmark
and its application to unstructured matrices. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC '14). IEEE Press, Piscataway, NJ, USA, 945-955. DOI: https://doi.org/10.1109/SC.2014.82
• E. Phillips and M. Fatica. 2014. A CUDA Implementation of the High Performance Conjugate Gradient Benchmark”. In High Performance Computing Systems. Performance Modeling, Benchmarking and Simulation, ser. Lecture Notes in Computer Science. Springer, Cham, pp. 68-84. Available: https://link.springer.com/chapter/10.1007/978-3-319-17248-4_4
• K. Kumahata et al. 2016. High-Performance conjugate gradient performance improvement on the K computer. In The International Journal of High Performance Computing Applications, vol. 30, no. 1, pp. 55—70. Available: https://doi.org/10.1177/1094342015607950
• X. Zhang et al. 2014. Optimizing and Scaling HPCG on Tianhe-2: Early Experience. In Algorithms and Architectures for Parallel Processing, ser. Lecture Notes in Computer Science, Springer, Cham, pp 28-41. Available: https://link.springer.com/chapter/10.1007/978-3-319-11197-1_3
4 © 2018 Arm Limited
Multi-level task dependency graph
• Nodes in the same level of the graph can be processed in parallel
• How to:
1. Add node 0 to the level 1
2. Mark node 1 as visited
3. Close level 1
4. Check neighbors of nodes in previous level to see if dependencies are fulfilled
1. If yes, add node to the level and mark node as visited
2. If no, continue with the next node
5. Close level, add new level and go to 4 if no more nodes to process
Level 0: 0Level 1: 1Level 2: 2, 4Level 3: 3, 5Level 4: 6, 8Level 5: 7, 9Level 7: 10, 12Level 8: 11, 13Level 9: 14Level 10: 15
5 © 2018 Arm Limited
Block multi-coloring
• Blocks with the same color can be processed in parallel
• How to:1. Group N consecutive nodes in blocks2. Colorize blocks3. Reorder blocks and rows of blocks sharing the same color
6 © 2018 Arm Limited
Merging all together
Coarser levels
Finest level
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Intra-node performance
0.00
0.20
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0.60
0.80
1.00
1.20
1 2 4 8 16 28
Para
llel E
ffici
ency
OpenMP threads
Strong scaling Weak scaling Ideal
0.00
5.00
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25.00
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1 2 4 8 16 28
Rela
tive
perf
orm
ance
agai
nst 1
thre
ad
OpenMP threads
Strong scaling Weak scaling Ideal
• Experiments executed on a dual-socket state-of-the-art Arm platform
8 © 2018 Arm Limited
Multi-node performance
0.80
0.90
1.00
1.10
1.20
1.30
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1 2 3 4 5 6 7
Re
lati
ve P
erf
orm
an
ce a
ga
inst
MP
I-o
nly
va
nill
a
# Nodes
Optimized Vanilla
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1 2 3 4 5 6 7
Pa
ralle
l Eff
icie
ncy
# Nodes
Optimized Vanilla Ideal
• Optimized:• 8 MPI ranks per node• 7 OpenMP threads per MPI rank• 256x224x256
• Vanilla:• 56 MPI ranks per node• OpenMP disabled• 128x128x128
9 © 2018 Arm Limited
Summary
• The code is open-source• https://gitlab.com/arm-hpc/benchmarks/hpcg• We welcome contributions! !
• We can collaboratively improve things• Hand-made NEON code• Hand-made SVE code• Platform-specific optimizations• Network communication
• Further information about our code on the the Arm Community blog• https://community.arm.com/tools/hpc/b/hpc/posts/parallelizing-hpcg
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Thank YouDankeMerci�������GraciasKiitos감사합니다ध"यवादהדות
© 2018 Arm Limited