2 Aug GPU CPU OpenGL 14) DirectX 15) API GPGPU GPGPU GPU GPGPU GPGPU GPGPU FP GPGPU 2 GPU 3 GPU 4 GPGPU 5 6 GPU GPGPU 7 2. Govindaraju 16) nvidi

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1 Vol. 48 No. SIG x(acs 19) Aug GPGPU, GPGPUGeneral-Purpose Computation on Graphics Processing UnitsGPU GPGPU GPU GPGPU GPU GPGPU LU 3 GPU 20%GPU 10% GPU A Performance Model for Assisting Development of GPGPU Applications Shingo Ito,, Fumihiko Ino and Kenichi Hagihara GPGPU stands for general-purpose computation on graphics processing units (GPUs), aiming at applying the GPU to general problems beyond graphics problems. This paper presents a performance model for typical GPGPU implementations, which is capable of predicting the possibility of the acceleration achievable by the GPU. Our model focuses on the fact that most of GPGPU implementations deal with memory-intensive problems and have regular access to data. Based on this fact, we represent the entire performance as the transfer performance of data paths connecting main memory, video memory, and processors inside the GPU. Each of the transfer performance here is simply represented by a combination of bandwidth and latency, which are independent of GPGPU applications. We applied the model to an image filter and LU decomposition to estimate their performance on three generations of GPUs. We found that the model has a 20% error at the worst case. We think that the model is useful for estimating the possibility of typical GPU-accelerated implementations, because the observed errors are less than 10% if GPU cache does not have significant effects on performance. 1. GPU 1),2) Graphics Processing Unit GPU GPGPUGeneral-Purpose Computation on GPUs 3) 4) 6) 7) 8) 11) SSE 12) CPU Department of Computer Science, Graduate School of Information Science and Technology, Osaka University Presently with Capcom Co., Ltd. 1 GPGPU memory intensive GPU 9),10) GPGPU 13) GPU FP Fragment Processor SIMD 4) 1

2 2 Aug GPU CPU OpenGL 14) DirectX 15) API GPGPU GPGPU GPU GPGPU GPGPU GPGPU FP GPGPU 2 GPU 3 GPU 4 GPGPU 5 6 GPU GPGPU 7 2. Govindaraju 16) nvidia GeForce 7800 GTX 128KB GPU GPU GPU 2) GPGPU Buck 17) Brook Brook CPU GPU 1 T r K gpu K gpu 18) GPU GPU GPU GPGPU 3. GPU GPU 2) nvidia GeForce 8800G80 1 GPU FP VPVertex Processor 2) VP FP VP FP VP 1 GPGPU FP FP SIMD RGB

3 Vol. 48 No. SIG x(acs 19) GPGPU 3 Vertex processors (VPs) Fragment processors (FPs) Rasterizer Video memory 1 GPU Fig. 1 Overview of GPU architecture. L2 texture cache A FP 4 GPU CPU GPU G80 G80 VP FP 1 SPStreaming Processor SP VP FP G80 VP FP SP G80 VPFP 4 SP 4. GPGPU GPGPU I FP I O I FP O OpenGL 14) DirectX 15) API GPGPU 7) FP 2 I P 1, P 2,..., P I 5 Inputs: (1) texture I and (2) fragment programs P 1, P 2,..., P I, each accessing K pixels Output: texture O 1: Typical GPGPU program { 2: Send texture I from main memory to video memory; 3: foreach rendering pass 1 i I { 4: Bind texture I; 5: Set program P i to draw texture O; 6: foreach pixel 1 j J { // this loop is automatically parallelized 7: Execute P i for j on a fragment processor; 8: } 9: Swap texture I for texture O; 10: } 11: Send texture O from video memory to main memory; 12: } 13: float4 Program P 1(float2 coord:texcoord0, uniform samplerrect tex:texunit0):color 14: float4 p = texrect(tex, coord); 15: p = p + texrect(tex, coord + float2(-1,0)); 16: return p + texrect(tex, coord + float2(1,0)); 17: } 2 GPGPU Fig. 2 Processing flow of typical GPGPU implementations. T1 T3 3 Fig. 3 Performance model. T2 FP FP Cg 19) GLSL 20) OpenGL Shading Language Cg 2 K I O J S 2 3 K = 3 1

4 4 Aug Table 1 Notation. I J K S 1 B d T d 1 d 3 L d T d 1 d 3 T T 3 P i i 1 i I T 1 T 2 FP GPGPU GPGPU T T 1T 3 1 GPGPU IJK S B 1 B 3 L 1 L GPGPU FP B 1B 3 L 1 L 3 T T = T 1 + IT 2 + T 3 (1) T 1 T 3 1 T 1 = JS/B 1 + L 1 (2) T 2 = KJS/B 2 + L 2 (3) T 3 = JS/B 3 + L 3 (4) 3 C1. C2. FP C3. T (1) C1 6 C2 C3 Buck 17) T J(K gpu + T r ) 2 GPGPU K gpu IKS/B 2 IKS/B 2 GPGPU L 1 + IL 2 + L 3 T GPU FP 2 tex 20 GPGPU 1/6 tex 4 GPGPU tex C2 FP F FP1 A A = J/F T 2 J T 2 = (KS/B 2 + L 2)J/F F A GL FLOAT R32 NV 1 S 4 J 1/4 A 1/4 GL FLOAT RGBA32 NV FP

5 / Vol. 48 No. SIG x(acs 19) GPGPU 5 4 copy_op max_op quadtree_op divide_op row_op 16) 9) GPUFFTW GPUSort CG 21) GPULU 5) Clustering 11) 7) Alignment Morphlogy 22) GPGPU 5),7),9),11),16),21),22) Fig. 4 Rate of computation operation over texture load operation in GPGPU implementations 5),7),9),11),16),21),22). The number of instructions of some fragment programs depends on problem size but has the same rate. T 1 T 2 S 5.2 C3 T 1T 3 T 1 T 2 SIMD FP T 1 T 2 T 2 T 3 GPU flush 3),5),23) T 2 T 3 23) ) FP void cpuprogram(region &region, // TextureObject *texture, // BufferSpecifier &drawbuffer) // { glbindtexture(texture); // // T 1 StopWatch.Start(); // gltexsubimage(); // StopWatch.Stop(); // // T 2 cgglbindprogram(fragmentprogram); // (b) gldrawbuffer(drawbuffer); // glclear(gl COLOR BUFFER BIT); // StopWatch.Start(); glbegin(); glrecti(region); // glend(); glfinish(); // OpenGL StopWatch.Stop(); // T 3 StopWatch.Start(); glreadpixels(); // StopWatch.Stop(); } (a) CPU program // K 1 K = 3 float4 fragmentprogram(float2 coord:texcoord0, uniform samplerrect tex:texunit0):color { float4 out = texrect(tex, coord); out += texrect(tex, coord + float2(-1,0)); out += texrect(tex, coord + float2(1,0)); return out; } (b) Fragment program 5 Fig. 5 Pseudocode for parameter estimation. 1 GPU 25) max(t 1, T 2) B 2 L 2 J J I K 1 5(b)K T 2 K 1 J I

6 6 Aug Table 2 Experimental environment. GPU 6800 GTONV GTXG GTXG80 MB GB/s Gpixel/s VP 5 6 FP PCI Express 16X CPU Pentium GHz Pentium D 3.0 GHz Pentium GHz 3 Table 3 Application-specific parameter values. I J K S 22) morphology copy op N 2 u=0 4 N u 1 max op N 2 log (N u)/2 u=0 v=0 1 2 v 2 LU 5) quadtree op N 2 log (N+1 u) u=0 v=0 2 (N + 1 u)/2 v 2 4 divide op N 2 u=0 1 N u 1 copy op N 2 u=0 1 N 1 u 1 row op N 2 u=0 1 (N 1 u)2 3 glbegin glend T 2 K T 2 B 2 L 2 J = 1 K = 1 B 2 K 1 3 FP tex perturbation GPGPU z 2) 1 B 1 B 3 gltexsubimage glreadpixels L 1 L B 2 K K J K K = % GPGPU B ) LU 5) GPGPU GPGPU IJ K 3 nvidia GPUNV45 G70 G80 2 nvidia OpenGL GPU I = J = K

7 Vol. 48 No. SIG x(acs 19) GPGPU 7 GPU 4 Table 4 Machine-specific parameter values. GPU B 1 (MB/s) L 1 (µs) B 2 (MB/s) L 2 (µs) B 3 (MB/s) L 3 (µs) 6800 GTONV , GTXG , pbuffer 26) 8800 GTXG , LU 6800 GTONV , GTXG , , FBO 27) 8800 GTXG , , pbuffer 26) S = 4 K LU 5 5) 32 FBO 27) Frame Buffer Object S = 4 N J K 1 LU I K 816 B 2 B 1 B Win32 QueryPerformanceCounter QueryPerformanceFrequency B 3 PCI Express 4GB/s GPGPU FBO T T m T p 100(T p/t m 1) CPU K = GPU 450 6(a)CPU 4 10% K 5 T K T 3 T 2 T 3 T 2 K T 3 T 2 T 2 T GPU K = 1024 NV45 B G G GPU 7 LU G70 G80 10%NV45 N 20% L1 6 5 row op row op x y (x, y)(x, 0) (0, y) 2 (x, 0) FP L1 L1 row op row op

8 8 Aug ) K: %) ) K: %) ) K: %) (a) 6800 GTONV45 (b) 7800 GTXG70 (c) 8800 GTXG80 6 Fig. 6 Prediction results for morphological filter. GPU 5 Table 5 Breakdown of prediction results for morphological filter. K = 4 K = 8 K = 16 K = 32 K = 64 K = 128 K = 256 K = 512 K = 1024 T GTO T T NV45 T T GTX T G70 T T T T GTX T G80 T % 5% B 2 G70 G80 L1 L1 N N N 7 G80 G70 G B G80 L 2 6 B 2 G80 row op J I 3 (1) T L 2 L 2 G80 NV45 row op T 55%B 2 T LU B 2 L 2 GPU L B 2 GPUBench 28) 4 2 K = 4 1/61/3 T 2

9 Vol. 48 No. SIG x(acs 19) GPGPU 9 ) %) ) %) ) %) N: N: N: (a) 6800 GTONV45 (b) 7800 GTXG70 (c) 8800 GTXG80 Fig. 7 7 LU Prediction results for LU decomposition. GPU 6 LU Table 6 Breakdown of prediction results for LU decomposition. N = 128 N = 256 N = 512 N = 1024 N = 2048 T copy op max op quadtree op GTO divide op NV45 row op T T T T copy op max op quadtree op GTX divide op G70 row op T T T T copy op max op quadtree op GTX divide op G80 row op T T T GPGPU GPGPU 7 4 GPGPU LU GPGPU GPU 1 GPU 7. GPGPU GPGPU

10 10 Aug Bandwidth (GB/s) Sequential Random Bandwidth (GB/s) Sequential Random Bandwidth (GB/s) Sequential Random (a) 6800 GTONV45 (b) 7800 GTXG70 (c) 8800 GTXG80 Fig. 8 8 B 2 Bandwidth B 2 with different access patterns. 7 GPGPU 5),7),9),11),16),21),22),28) Table 7 Classification of access patterns in GPGPU implementations 5),7),9),11),16),21),22),28). (x, y) (X, Y )* LU 5) divide op 1 LU copy op CG 21) Copy 1 (x, y) SelfComponentMultiply GPUFFTW 16) copy 2 GPU-Sort 9) laststepfptext (x, 0)(0, y) (x, y) LU row op 2 LU max op 1 (x + X, y + Y ) (x, y) CG sumreduction GPUFFTW copy {(x + x, y + y ) X x, y X} 22) 2 (x 1, y)(x 1, y + 1)(x, y + 1) Alignment 7) 2 lfillr {(4x + x, y) 0 x X} GPU-Sort lfillg lfillb 2 lfilla I 1,..., I n I 1 (x, y),..., I n (x, y) (X x, y) (x, y) (X x, Y y) (x, y) I 1 (I 2 (x, y), I 3 (x, y )) *X Y LU CG quadtree op scaledadd ComponentMultiply 1 n = 2 GPUBench 28) sequential 2 Clustering 11) n = 4 GPU-Sort minfptext maxfptest Combine two channels lastminusonestepfptext 2 CG MatrixVectorMultiplication 1 GPUBench random 2 FP GPGPU LU 3 GPU 20%GPU 10%

11 Vol.48 No.SIGx(ACS19) GPGPU 11 GPU 5.2 CPU GPU 6) B ) Pharr, M. and Fernando, R.(eds.): GPU Gems 2: Programming Techniques for High- Performance Graphics and General-Purpose Computation, Addison-Wesley, Reading, MA (2005). 2) Montrym, J. and Moreton, H.: The GeForce 6800, IEEE Micro, Vol.25, No.2, pp (2005). 3) Owens, J.D., Luebke, D., Govindaraju, N., Harris, M., Krüger, J., Lefohn, A.E. and Purcell, T.J.: A Survey of General-Purpose Computation on Graphics Hardware, Computer Graphics Forum, Vol.26, No.1, pp (2007). 4) Fatahalian, K., Sugerman, J. and Hanrahan, P.: Understanding the Efficiency of GPU Algorithms for Matrix-Matrix Multiplication, Proc. 19th SIGGRAPH/EUROGRAPHICS Workshop Graphics Hardware (GH 04), pp (2004). 5) Galoppo, N., Govindaraju, N.K., Henson, M. and Manocha, D.: LU-GPU: Efficient Algorithms for Solving Dense Linear Systems on Graphics Hardware, Proc. Int l Conf. High Performance Computing, Networking, Storage and Analysis (SC 05) (2005). 12 pages (CD- ROM). 6) CPU GPU GEMM Vol.47, No.SIG12(ACS15), pp (2006). 7) Liu, W., Schmidt, B., Voss, G. and Müller- Wittig, W.: Streaming Algorithms for Biological Sequence Alignment on GPUs, IEEE Trans. Parallel and Distributed Systems, (to appear). 8) Govindaraju, N.K., Lloyd, B., Wang, W., Lin, M.C. and Manocha, D.: Fast Computation of Database Operations using Graphics Processors, Proc. ACM SIGMOD Int l Conf. Management of Data (SIGMOD 04), pp (2004). 9) Govindaraju, N.K., Raghuvanshi, N., Henson, M., Tuft, D. and Manocha, D.: A Cache- Efficient Sorting Algorithm for Database and Data Mining Computations using Graphics Processors, Technical Report TR05-016, University of North Carolina-Chapel Hill (2005). 10) Greß, A. and Zachmann, G.: GPU-ABiSort: Optimal Parallel Sorting on Stream Architectures, Proc. 20th IEEE Int l Parallel and Distributed Processing Symp. (IPDPS 06) (2006). 10 pages (CD-ROM). 11) Takizawa, H. and Kobayashi, H.: Hierarchical parallel processing of large scale data clustering on a PC cluster with GPU co-processing, The J. Supercomputing, Vol.36, No.3, pp (2006). 12) Klimovitski, A.: Using SSE and SSE2: Misconceptions and Reality, Intel Developer Update Magazine (2001). 13) Khailany, B., Dally, W.J., Kapasi, U.J., Mattson, P., Namkoong, J., Owens, J.D., Towles, B., Chang, A. and Rixner, S.: IMAGINE: MEDIA PROCESSING WITH STREAMS, IEEE Micro, Vol.21, No.2, pp (2001). 14) Shreiner, D., Woo, M., Neider, J. and Davis, T.: OpenGL Programming Guide, Addison- Wesley, Reading, MA, fifth edition (2005). 15) Microsoft Corporation: DirectX, Asm Shader Reference (2005). library/default.asp?url=/library/en-us/direct x9 c/directx/graphics/reference/reference.asp. 16) Govindaraju, N.K., Larsen, S., Gray, J. and Manocha, D.: A Memory Model for Scientific Algorihms on Graphics Processors, Proc. High Performance Networking and Computing Conf. (SC 06) (2006). 10 pages (CD-ROM). 17) Buck, I., Foley, T., Horn, D., Sugerman, J., Fatahalian, K., Houston, M. and Hanrahan, P.: Brook for GPUs: Stream Computing on Graphics Hardware, ACM Trans. Graphics, Vol.23, No.3, pp (2004). 18) Sheaffer, J.W., Luebke, D. and Skadron, K.: A Flexible Simulation Framework for Graphics Architectures, Proc. 19th SIG- GRAPH/EUROGRAPHICS Workshop Graphics Hardware (GH 04), pp (2004). 19) Mark, W.R., Glanville, R.S., Akeley, K. and Kilgard, M.J.: Cg: A system for programming graphics hardware in a C-like language, ACM Trans. Graphics, Vol.22, No.3, pp (2003). 20) Rost, R.J.: OpenGL Shading Language,

12 12 Aug Addison-Wesley, Reading, MA, second edition (2006). 21) Corrigan, A.: Implementation of Conjugate Gradients (CG) on Programmable Graphics Hardware (GPU) (2005). ens.edu/%7equynh/student-work/acorrigan g pu.htm. 22) GPU 10 Visual Computing CAD pp (2006). 23) nvidia Corporation: Fast Texture Downloads and Readbacks using Pixel Buffer Objects in OpenGL, Technical Brief TB v01, nvidia Corporation (2005). download.nvidia.com/developer/papers/2005/ Fast Texture Transfers /Fast Texture Transfer s.pdf. 24) Xu, F. and Mueller, K.: Ultra-Fast 3D Filetered Backprojection on Commodity Graphics Hardware, Proc. 1st IEEE Int l Symp. Biomedical Imaging (ISBI 04), pp (2004). 25) Ujaldon, M. and Saltz, J.: Exploiting parallelism on irregular applications using the GPU, Proc. Int l Conf. Parallel Computing (ParCo 05), pp (2005). 26) OpenGL Extension Registry: WGL ARB pbu ffer (2002). pbuffer.txt. 27) OpenGL Extension Registry: GL EXT frame buffer object (2006). cts/ogl-sample/registry/ext/framebuffer obj ect.txt. 28) Buck, I., Fatahalian, K. and Hanrahan, P.: GPUBench: Evaluating GPU Performance for Numerical and Scientific Applications, Proc. 1st ACM Workshop General-Purpose Computing on Graphics Processors (GP 2 04), p.c-20 (2004). ( ) ( ) GPU HiPC SAC- SIS HiPC SACSIS 04

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