On the limits of (and opportunities for?) GPU acceleration
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1 On the limits of (and opportunities for?) GPU acceleration Aparna Chandramowlishwaran, Jee Choi, Kenneth Czechowski, Murat (Efe) Guney, Logan Moon, Aashay Shringarpure, Richard (Rich) Vuduc HotPar 10, Berkeley June 15, 2010
2
3 Q: Port to GPU? (Posed to me by Scott Klasky at ORNL) A: Given roughly same level of tuning & power*, GPU CPU Meta-analysis, for semi-irregular sci. comp. + data analytics apps (sparse iterative + direct solvers; tree-based particle methods) 3
4 Summary of limits Bandwidth-bound: Aggregate bandwidth < 3x, restricted access patterns Compute-bound: 5 to 10x peak potential, but there is a multithreading granularity mismatch PCIe: Will architects replicate GPU memory system in on-die CPU/GPU? Productivity: To 0th order, tuning required on all platforms I.e., Bailey s Rule #6 4
5 Limitations of this meta-analysis Mix of partial results, very rough back-of-the envelope, apples vs. oranges But: It s all fruit My Big Fat Greek Wedding Narrow: Scientific computing? (yawn) But: More physically realistic games & graphics, signal analysis, data analytics Limited to today s platforms, and excludes Fermi. What about tomorrow? But: Prediction is very difficult, especially if it's about the future. N. Bohr 5
6 Other voices Vishkin, et al., HotPar 10 poster! Bordawekar, et al. (IBM). Believe it or Not! Multi-core CPUs Can Match GPU Performance for FLOP-intensive Application! IBM Technical Report RC24982, April Lee, et al. (Intel). Debunking the 100X GPU vs. CPU Myth: An Evaluation of Throughput Computing on CPU and GPU. ISCA, June
7 Performance and productivity expectations 7
8 Easy to write in Nesl, but at what cost?. 100 Lines of code Time Nesl (16-cores) C (1-core) Cilk++ (16-cores) Tuned library (16-core) CUDA (GPU) Worth the effort? Algorithm: Parallel sorting 8
9 (7.2, 1030) (9.1, 933) 256 Gflop/s (3.3, 86) Platform a Fermi a Nehalem a T10P Single-precision 1:1 socket 2 1/8 1/4 1/ Intensity (flop : byte)
10 1024 (7.2, 1030) (9.1, 933) ~ 8x (Case study 3) ~ 12x (Case study 2) 128 (3.3, 86) Gflop/s ~ 4x (Case study 1) Platform a Fermi a Nehalem a T10P Single-precision 1:1 socket 2 1/8 1/4 1/ Intensity (flop : byte)
11 (3.6, 515) 256 ~ 2 to 12x 128 Gflop/s (0.8, 78) (1.7, 43) Platform a Fermi a Nehalem a T10P ~ 3 to 4x Double-precision 1:1 socket 2 1/8 1/4 1/ Intensity (flop : byte)
12 Case study 1: Sparse iterative solvers S. Williams, N. Bell, J. Choi, M. Garland, L. Oliker, R. Vuduc. SpMV on MC & Acc. In BDK book (2010). 12
13 Anatomy of a sparse iterative solver do { y A*x SpMV } while (!converged) Bottleneck: Sparse matrix-vector multiply (SpMV) Memory bandwidth-limited (stream A): GPU / CPU ~ 3x 13
14 20 18 Double Gflop/s Platform Nehalem GTX 285 Nehalem (tuned) Dense Protein Spheres Cantilever WindTunnel Harbor QCD Ship Economics Epidemiology Accelerator Circuit Webbase S. Williams, N. Bell, J. Choi, M. Garland, L. Oliker, MatrixR. Vuduc. SpMV on MC & Acc. In BDK book (2010). LP 14
15 20 18 Double Gflop/s ~ 6 to 7x Platform Nehalem GTX 285 Nehalem (tuned) Dense Protein Spheres Cantilever WindTunnel Harbor QCD Ship Economics Epidemiology Accelerator Circuit Webbase S. Williams, N. Bell, J. Choi, M. Garland, L. Oliker, MatrixR. Vuduc. SpMV on MC & Acc. In BDK book (2010). LP 15
16 20 18 Double Gflop/s ~ 2.1x (vs. ~ 3x bandwidth) Platform Nehalem GTX 285 Nehalem (tuned) Dense Protein Spheres Cantilever WindTunnel Harbor QCD Ship Economics Epidemiology Accelerator Circuit Webbase S. Williams, N. Bell, J. Choi, M. Garland, L. Oliker, MatrixR. Vuduc. SpMV on MC & Acc. In BDK book (2010). LP 16
17 Beyond the kernel Optimal data structures differ between CPU & GPU Startup, transfer cost In distributed memory, need to transfer vectors PCIe limits Need ~ 100 iterations to break even, ~ 840 to get 2x on actual solver Big or not? Depends on app & input 17
18 Case study 2: The Fast Multipole Method (1) Lashuk, et al., SC 09. (2) Chandramowlishwaran, Williams, et al., IPDPS
19 Blood cell simulation (movie) In 2-D with deformations 19
20 Anatomy of an FMM Want: All pair interactions among green dots O(n 2 ) FMM idea: Build tree, traverse & prune (approx.) O(n log n), with accuracy guarantee Bottleneck: Little all-pair interactions (b 2 ) among leaves High compute intensity: 12x possible? 20
21 The story Baseline: Lashuk, et al., SC 09 FMM that scales to 100k cores of Kraken UTK Good overall scalability, but low within-node performance Try GPUs? Gumerov & Duraiswami (JCP 08) suggest 30 60x speedups on GPUs We successfully replicate on 256 GPU system at UIUC (1 MPI task / GPU) But, stubborn student (Aparna C.) is skeptical of speedup 21
22 Speedup over Nehalem Baseline Code Baseline Opt Opt+Par Nehalem C1060 C1060 x 2 Platform
23 53 0.9x Speedup over Nehalem Baseline x 31 Code Baseline Opt Opt+Par Nehalem C1060 C1060 x 2 Platform
24 Recall: Anatomy of an FMM Want: All pair interactions among green dots O(n 2 ) FMM idea: Build tree, traverse & prune (approx.) O(n log n), with accuracy guarantee Bottleneck: Little all-pair interactions (b 2 ) among nodes High compute intensity: 12x possible? 24
25 Direct O(n^2) n body algorithm Platform AMD Barcelona Gflop/s 200 Intel Harpertown NVIDIA Tesla C1060 NVIDIA Tesla C870 STI PowerXCell/8i No. of Particles
26 Direct O(n^2) n body algorithm 500 ~ 500 Gflop/s (!) Platform AMD Barcelona Gflop/s 200 Intel Harpertown NVIDIA Tesla C1060 NVIDIA Tesla C870 STI PowerXCell/8i No. of Particles
27 Direct O(n^2) n body algorithm 500 ~ 500 Gflop/s (!) Platform AMD Barcelona Gflop/s 200 Intel Harpertown NVIDIA Tesla C1060 NVIDIA Tesla C870 STI PowerXCell/8i No. of Particles
28 Case study 3: Sparse direct solvers (1) M. Efe Guney, Ph.D. Thesis, Georgia Tech, May 10. (2) Guney, Czechowski, et al. (in progress) 28
29 Anatomy of a sparse direct solver Sparse Cholesky factorization, A = L L T, where A & L are sparse Mixed compute intensity, average of ~ 4 flops : byte for sample problem 29
30 Real elimination tree example Independent subtrees may be processed in parallel. 30
31 Depth Flops (%) Cumulative flops (%) Depth
32 Finer-grained dependencies Colored circles on the right are BLAS calls on operands of varying size. 32
33 Fraction of time in BLAS calls 0.3 % ops dgemm dpotrf dsyrk dtrsm
34 flop : byte Fraction of flops /8 1/4 1/ BLAS dgemm dpotrf dsyrk dtrsm Intensity mix
35 BLAS Depth Depth dgemm dpotrf dsyrk dtrsm % ops
36 flop : byte % ops /8 1/41/ /8 1/41/ /8 1/41/ BLAS dgemm dpotrf dsyrk dtrsm Depth
37 Double-precision Gflop/s! 40! 35! 30! 25! 20! 15! 10! 5! 28.1! 26.6! 23.5! 20.1! 22.4! 21.7! 17.1! 14.1! 35.2! 33.5! 30.8! 30.2! 31.0! 25.2! 1 core (4-core ~ 2-4x) 9.5! 9.8! 10.3! 10.3! 10.6! 10.9! 11.0! 0! S15x15x50! F15x15x50! S30x30x30! S100x50x13! F30x30x30! S50x50x50! F45x45x45! Frontal matrix size! GPU Gflop/s! + copy! GPU Gflop/s! (no copy)! 1-core CPU Gflop/s! + copy!
38 Summary: Definite potential, but no magic For a set of semi-irregular computations, 1 GPU 1 to 2 CPUs. Study heterogeneous computing, but scale-back expectations. Barriers? Bandwidth-bound: Aggregate GPU : CPU bandwidth < 3x PCIe: Will we really replicate GPU memory system in on-die CPU/GPU? Compute-bound: 5 to 10x potential, but how? E.g., FMM granularity mismatch Productivity: To 0th order, tuning required on all platforms (Bailey s Rule #6) 38
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