Spmv PowerPoint PPT Presentations

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

Kaushik Datta, Mark Hoemmen, Marghoob Mohiyuddin, Shoaib Kamil, Rajesh Nishtala, ... 8x8 dense substructure: exploit this to limit #mem_refs ...

Automatic Performance Tuning and Sparse-Matrix-Vector-Multiplication (SpMV) James Demmel www.cs.berkeley.edu/~demmel/cs267_Spr10 * TO DO: Replace this with ex11 spy ...

Minimizing Communication in Numerical Linear Algebra www.cs.berkeley.edu/~demmel Sparse-Matrix-Vector-Multiplication (SpMV) Jim Demmel EECS & Math Departments, UC ...

CS267 Lecture 15 Automatic Performance Tuning and Sparse-Matrix-Vector-Multiplication (SpMV) James Demmel www.cs.berkeley.edu/~demmel/cs267_Spr14

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Tuning Sparse Matrix Vector Multiplication for multi-core SMPs ... Examined Sparse Matrix Vector Multiplication (SpMV) kernel. Important HPC kernel ...

Auto-tuning Sparse Matrix-Vector Multiplication (SpMV) ... you trade free (always pay for it) cache-coherency traffic for additional memory ...

Tuning becoming more difficult over time. Performance ... Statistical models of performance. BIPS. BIPS. Matrix-vector multiply kernel: y(i) y(i) A(i,j)*x(j) ...

Best choice can depend on knowing a lot of applied mathematics and ... Algorithm and its implementation may strongly depend on data only known at run-time ...

Title: Benchmarking Sparse Matrix-Vector Multiply (in just 5 minutes) Author: Office 2004 Test Drive User Last modified by: CK Created Date: 10/31/2006 8:34:20 AM

Impact on library designs: Sparse BLAS, Trilinos, PETSc, ... TSP reordering to create dense blocks (Pinar '97; Moon, et al. ' 04) Extra Slides ...

Multiply a dense vector by a sparse matrix (one whose entries are mostly zeroes) ... Since dimension range is so huge, restrict dimension to powers of 2 ...

bebop.cs.berkeley.edu. Outline. Motivation for Automatic Performance Tuning ... BEBOP project addresses this. Tuning Dense BLAS PHiPAC. Tuning Dense BLAS ATLAS ...

Autotuning Sparse Matrix and Structured Grid Kernels Samuel Williams1,2, Richard Vuduc3, Leonid Oliker1,2, John Shalf2, Katherine Yelick1,2, James Demmel1,2, Jonathan ...

Adaptable benchmarks for register blocked sparse. matrix-vector multiplication ... Tyler Berry (tyler@arete.cc) Felipe Gasper (fgasper@fgmusic.org) Resources. BeBOP: ...

Title: PowerPoint Presentation Author: WSE Last modified by: Nicola Mastronardi Created Date: 5/7/2002 1:59:17 PM Document presentation format: Presentazione su ...

Computer representations of sparse matrices. Sparse matrix-vector ... 'triplets' format ({i, j, val}) is not sufficient . . . Storage: 2*NNZ integers, NNZ reals ...

B E R K E L E Y I N S T I T U T E F O R P E R F O R M A N C E S T U D I E S. C O M P U T A T I O N A L R E S E A R C H D I V I S I O N ...

Jack Dongarra, Victor Eijkhout, Julien Langou, Julie Langou, Piotr Luszczek, Stan Tomov ... calls to ILAENV() to get block sizes, etc. Not systematically tuned ...

Chapter 7 Multicores, Multiprocessors, and Clusters

Titanium

Debunking the 100X GPU vs. CPU Myth: An Evaluation of Throughput Computing on CPU and GPU Presented by: Ahmad Lashgar ECE Department, University of Tehran

Hide the complex process of parallel tuning while exposing its cost ... Hides complexity of run-time tuning. Low ... The parallelism is hidden under the covers ...

Parallel machines are too hard to program. Users 'left behind' ... Carrie Fei. Ben Liblit. Robert Lin. Geoff Pike. Jimmy Su. Ellen Tsai. Mike Welcome (LBNL) ...

Best choice can depend on knowing a lot of applied mathematics and computer science ... At run-time, algorithm choice may depend only on few parameters ...

Algorithms that attain them (all dense linear algebra, some sparse) ... Can we attain these lower bounds? Do conventional dense algorithms as implemented in ...

... (bad for superscalar), Difficult to exploit DLP(bad for SIMD) ... power of 2 register blocking CSR/COO format 16b/32b indices etc Side effect: ...

OSKI: A Library of Automatically Tuned Sparse Matrix Kernels ... Design point: user calls 'tune' routine explicitly. Exposes cost ...

... time tuning cost: up to ~40 mat-vecs. Dominated by conversion ... Types 'registered' at run-time. Module interface includes kernels, conversion, ... Kernels ...

Chapter 7 Multicores ... software Devising appropriate architectures Many reasons for optimism ... Time 7.8 Introduction to Multiprocessor Network Topologies ...

256.00 22478.70 22686.59 21920.92 22321.99 23758.26 113166.46 256.00 0.00 0.00 256.00 51.59 13206.16 256.00 53.41 13672.69 256.00 64.17 16427.49 256.00 56.57 14482 ...

[Frigo, Leiserson, Prokop, Ramachandran,99] CS267 Lecture 2 ... some redundant computation Much prior work See bebop.cs ... Sun Ultra2 Model 2200. SGI ...

Destination vector elements for stored block. Source vector elements for transpose block ... Current & Future Directions. Parallel SMP Kernels. Multi-threaded ...

C O M P U T A T I O N A L R E S E A R C H D I V I S I O N. BIPS. BIPS ... Samuel Williams1,2, Richard Vuduc3, Leonid Oliker1,2, ...

The Parallel Computing Laboratory: A Research Agenda based on the Berkeley View Krste Asanovic, Ras Bodik, Jim Demmel, Tony Keaveny, Kurt Keutzer, John Kubiatowicz ...

Title: Optimizing Matrix Multiply Author: Kathy Yelick Description: Slides by Jim Demmel, David Culler, Horst Simon, and Erich Strohmaier Last modified by

Goal: Algorithms that communicate as little as possible for: ... Grey Ballard, UCB EECS. Ioana Dumitriu, U. Washington. Laura Grigori, INRIA. Ming Gu, UCB Math ...

The Roofline Model: A pedagogical tool for program analysis and optimization ParLab Summer Retreat Samuel Williams, David Patterson samw@cs.berkeley.edu

256.00 22478.70 22686.59 21920.92 22321.99 23758.26 113166.46 256.00 0.00 0.00 256.00 51.59 13206.16 256.00 53.41 13672.69 256.00 64.17 16427.49 256.00 56.57 14482 ...

Title: Optimizing Matrix Multiply Author: Kathy Yelick Description: Slides by Jim Demmel, David Culler, Horst Simon, and Erich Strohmaier Last modified by

Fully Buffered DRAM. 4MB Shared L2 (16 way) 42.7GB/s (read), 21.3 GB/s (write) 8K D ... Shared L2. Core2. FSB. Fully Buffered DRAM. 10.6GB/s. Core2. Chipset ...

... existing optimizations, Auto-tuning automates ... Used newer architectures (Opteron, Power5, Itanium2) ... Design auto-tuners for an arbitrary number of threads ...

... A. Gupta 04/13/09 CS267 Lecture 20 Multigrid for nonlinear elastic analysis of bone Mechanical testing for material properties ... mathematical properties of T ...

Based on lectures by James Demmel ... Graph Partitioning Laura Grigori and James Demmel www.cs.berkeley.edu/~demmel/cs267_Spr15

Based on s by Jim Demmel and others

Susan Blackford, UT. Jaeyoung Choi, Soongsil U. Andy Cleary, LLNL. Ed ... Jack Dongarra, UT/ORNL. Sven Hammarling, NAG. Greg Henry, Intel. Osni Marques, NERSC ...

... TOPS 500, by year .13M. 6768 .3. 1 .28. Intel Paragon XP/S MP. 1995. ... Parallel time = O( tf N3/2 / P tv ( N / P1/2 N1/2 P log P ) ) Performance model 2 ...

Title: CS267: Graph Partitioning Author: Kathy Yelick Description: Based on lectures by James Demmel Last modified by: James Demmel Created Date: 1/20/1997 7:06:50 AM

L11: Sparse Linear Algebra on GPUs CS6963 * Administrative Issues Next assignment, triangular solve Due 5PM, Tuesday, March 15 handin cs6963 lab 3

0.00 0.00 0.00 27.87 27.93 28.27 28.02 27.16 all forward fft. 0.00 0.00 0.00 4.44 3.00 2.00 3.00 4 ... Extra s Radix: Stream Broadcast Problem What s ...

One core is a conventional cache based PPC. The other 8 are local memory based SIMD ... 500W blades (2 chips DRAM network) 6. SPE Architecture. 128b SIMD ...

... size & bandwidth per core. Symbiosis of architecture and ... (Dual-core Opteron)? Open Shapes = Existing Logarithmic Algorithm (Gibson/Bruck)? Solid Shapes ...

'The Berkeley View' (Asanovic et al.) Motifs form key computational patterns ... FFT (Lecture 21, Horst Simon) Multigrid. 04/13/09. CS267 Lecture 20. Solving PDEs ...

Iteratively compute set of methods that can complete. CanComplete f ... Definition: A parallel execution must behave as if it were an interleaving of ...