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Automatic Performance Tuning of SpMV on GPGPU Xianyi Zhang Lab of Parallel Computing Institute of Software Chinese Academy of Sciences

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Presentation on theme: "Automatic Performance Tuning of SpMV on GPGPU Xianyi Zhang Lab of Parallel Computing Institute of Software Chinese Academy of Sciences"— Presentation transcript:

1 Automatic Performance Tuning of SpMV on GPGPU Xianyi Zhang Lab of Parallel Computing Institute of Software Chinese Academy of Sciences zxy@mail.rdcps.ac.cn

2 Outline  Motivation  SpMV Introduction  AMD Stream Computing  GOSpMV Overview  GOSpMV Performance Evaluation  Conclusion & Future Work

3 Motivation  Sparse Matrix-Vector Multiplication (SpMV) y=y+Ax  The important kernel in scientific applications PDE solver, simulation, etc.  Low performance Irregular memory access pattern

4 Motivation  GPU  Huge computation power Jason Yang, James Goodman. Symmetric Key Cryptography on Modern Graphics Hardware. http://ati.amd.com/technology/streamcomputing/asiacrypt2007.pdf http://ati.amd.com/technology/streamcomputing/asiacrypt2007.pdf

5 SpMV Introduction  CSR (Compressed Sparse Row) A_val=[1,2,4,1] A_col=[0,2,1,2] A_ptr=[0,2,3,4] for(i = 0; i < n ; i++) { value = 0; for(j = A_ptr[i]; j < A_ptr[i+1] ; j++) value = value + A_val[j]*x[A_col[j]]; y[i] += value; } x is accessed irregularly x is accessed indirectly

6 SpMV Introduction  BCSR (Block Compressed Sparse Row)  BCSR 2 × 3

7 AMD Stream Computing  Programming Model AMD Stream Computing User Guide

8 AMD Stream Computing  AMD Brook+ AMD Stream Computing User Guide

9 GOSpMV Overview  GOSpMV Software Architecture

10 GOSpMV Overview  BCSR SpMV implementation on GPGPU

11 GOSpMV Overview  Automatic Performance Tuning

12 GOSpMV Overview  Off-line GPGPU Benchmark Dense matrix (different size) Every BCSR block size

13 GOSpMV Overview  Run-Time Evaluation(search optimal BCSR block size) Input: Sparse Matrix A, GPGPU Benchmark data P dense (block-format, nz d ) Output: the maximum P (A, block-format, σ), optimal BCSR block size For each BCSR r × c block, do calculate fill ratio f Erc (A, σ) with sample rate σ P sp (block-format, nz EBCSR )= P dense (block-format, nz d ), nz d is nearest to nz EBCSR P (A, block-format, σ) = P (block-format, nz EBCSR )/ f Erc (A, σ) done

14 GOSpMV Performance Evaluation  Test box  Intel Pentium Dual Core E2160/1.8GHz, 2.0GB memory  GPU AMD Radeon HD 3690 (RV670), theoretical peak:428.8 GigaFlOPS (single precision)  AMD Stream SDK v1.1-beta  Ubuntu 8.04, Linux 2.6.24, gcc 4.2.3  Test matrices  8 sparse matrices, different size (small, medium, large) Small (nonzeros < 100,000) Medium (100,000 < nonzeros < 1,000,000) Large (nonzeros >= 1,000,000)  Matrix Market and UF Sparse Matrix Collection.

15 GOSpMV Performance Evaluation  Test matrices

16 GOSpMV Performance Evaluation  AMD Radeon HD 3690 Result  SpMV BCSR on GPGPU (1500 iterations)

17 GOSpMV Performance Evaluation  Different iterations (100,300,500,1000,1500)

18 GOSpMV Performance Evaluation  The automatic performance tuning (1500 iterations)  The average speedup: 3.11

19 Conclusion  GOSpMV Performance Speedup  AMD Radeon HD 3690 average: 3.11, max: 5.96, 1500 iterations  GOSpMV is suited for  Medium matrices, Large matrices  Iteration number>= 300  Regular matrices (low fill ratio)  In general, GOSpMV selects the better BCSR block size by automatic performance tuning technology.

20 Future Work  Double precision  Support other BCSR block size (e.g. 8x8)  New HW (AMD RV770)  Automatic performance tuning strategy  Re-ordering matrix

21 Thank you ！ Ｑ＆Ａ

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