Benchmarking SpMV on Many-Core Architecture

Transcription

1 Bechmarkig SpMV o May-Core Architecture Biwei Xie ad Zhe Jia Istitute of Computig Techology Chiese Academy of Scieces Priceto Uiversity

2 Why Bechmarkig? To Measure Is To Kow -- William Thomso (Lord Kelvi)

3 We have a implemetatio

4 But, what if

5 Why SpMV?

6 SpMV: Sparse matrix-vector multiplicatio Give a sparse m matrix A ad a dese 1 vector x: y = A x: = A x y

7 HPC SpMV Applicatio Scearios Various liear algebra algorithms: CG (Cojugate Gradiets) Graph Computig Page Rak, BFS, etc. CNN Covolutio

8 Factors importat to SpMV performace Characteristics of the matrix Data scale Sparsity Sparse Patter SpMV Methods CSR, CSC,DIA, COO,CSR5,CVR, ELL,ESB,Merge (dozes) Parallelizatio, Vectorizatio, Blockig Platform X86, ARM, GPU Differet architecture desig impact the fial performace a lot. How to locate the best SpMV method for a give sparse matrix o a specific architecture?

9 Bechmarkig Methodology

10 Sparse Matrix (Data Set) Sparse Matrix 1,500+ sparse matrices from UFL (discard small matrices) Various sparse patters ad data scales Wikipedia -Talk Web-Google ASIC100k Wid Tuel Ecoomics Circuit5M Catilever Ga41As41H72 higgs-twitter Amazo-0312

11 SpMV algorithms: SpMV Methods 27 SpMV implemetatios. From high-quality research (ICS, SC, CGO ) From commercial/ope-source packages Widely used (CSR, COO ) CSR: By rows CSC: By colums BSR: By blocks DIA: By diagoals CVR: By multi-rows ELL: By blocks & rows

12 Platforms (Architectures) Architecture (May-core) Represetative may-core architectures: Itel Xeo Phi, GPGPU Much differet architecture desig: Itel Xeo Phi: KightsLadig,CMP+ SIMD GPGPU: NVidia Tesla M40, SIMT

13 Performace o CPU

14 Performace o CPU (Cotiued)

15 Observatios o CPU CSR, IE, CSR5 ad CVR, show good performace o both small ad large sparse matrices with various sparse patters. COO, CSC, ad DIA, which are widely used i realworld scearios, show much poorer performace. BSR, ESB-d ad ESB-s are sesitive to the sparse patters

16 Performace o GPU

17 Observatios o GPU BSR, HYB, ELL ad DIA are sesitive to the sparse patters Merge method is stable ad isesitive to sparse patters

18 Best Methods Distributio No sigle SpMV method is suitable for all sparse matrices Some methods show much better performace tha others CPU GPU

19 O Phi: O GPU: Optimal Methods Distributio CVR ad CSR5 are the optimal for more tha 84% data sets The optimal method is quite scattered. CSR5 occupies 56%.

20 Sub-optimal methods: Sub-optimal Slightly worse thathe best performace

21 Xeo Phi: CPU CVR is the best o more tha 82% matrices with less tha 20% performace loss to the optimal. Widely used SpMV methods, likecsr,csc, COO,DIAisot as good as expected. 100% 80% Optimal Sub-optimal(+10%) Sub-optimal(+20%) 60% 40% 20% 0% CVR CSR5 IE CSR VHCC ESB-s DIA BSR ESB-d CSC COO

22 Tesla: GPGPU CSR5 achieves sub-optimal o 65% sparse matrices with less tha 20% performace loss. ELL ad its derivative show modest performace 100% 80% Optimal Sub-optimal(+10%) Sub-optimal(+20%) 60% 40% 20% 0%

23 Correlatio : Correlatio Aalysis Aalyze the correlatio betwee SpMV performace ad the features(data scale, sparse patter ad etc.) Pearso correlatio coefficiet rage -1 to 1: 1: positive liear correlatio, 0: o liear correlatio, 1: total egative liear correlatio

24 Data scale: Correlatio Aalysis Withthe umber of o-zero elemets icreasig, the performace of most SpMV methods icrease.

25 Desity: Correlatio Aalysis Most SpMV methods show lower throughput whe the matrix is sparser.

26 Three factors: Coclusio Sparse matrix: sparse patter, data scale SpMV method: parallelizatio, vectorizatio, blockig Hardware platform: Xeo Phi, GPGPU Takig away: Certai methods ca achieve good performace for most data sets Some widely used methods, i.e., CSR, CSC, are ot as good as emergig oes For most SpMV methods, sparser matrix results i lower throughput Ope-source project: a bechmarkig framework, which supports almost all SpMV methods o Itel Xeo Phi ad GPGPU.

27 More result i the paper Comig soo

28 Thaks! Q&A

29 Slides for Defedig