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Don Batory, Bryan Marker, Rui Gonçalves, Robert van de Geijn, and Janet Siegmund Department of Computer Science University of Texas at Austin Austin, Texas DxT- 1

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Introduction Software Engineering (SE) Software Engineering (SE) largely aims at techniques, tools to aid masses of programmers whose code is used by hoards these programmers need all the help they can get Many areas where programming tasks are so difficult, only a few expert programmers – and their code is used by hoards these experts need all the help they can get too DxT- 2

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Our Focus is CBSE for… Dataflow domains: – nodes are computations – edges denote node inputs and outputs General: Virtual Instruments (LabVIEW), applications of streaming languages… Our domains: Distributed-Memory Dense Linear Algebra Kernels Parallel Relational Query Processors Crash Fault-Tolerant File Servers DxT- 3

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Approach CBSE Experts produce “Big Bang” spaghetti diagrams (dataflow graphs) We derive dataflow graphs from domain knowledge (DxT) When we have proofs of each step: Details later… DxT- 4

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State of Art for Distributed Memory D ense L inear A lgebra Kernels Portability of DLA kernels is problem: may not work – distributed memory kernels don’t work on sequential machines may not perform well choice of algorithms to use may be different cannot “undo” optimizations and reapply others if hardware is different enough, code kernels from scratch DxT- 5

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Why? Because Performance is Key! Applications that make DLA kernel calls are common to scientific computing: simulation of airflow, climate change, weather forecasting Applications are run on extraordinarily expensive machines time on these machines = $$ higher performance means quicker/cheaper runs or more accurate results Application developers naturally want peak performance to justify costs DxT- 6

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Distributed DLA Kernels Deals with SPMD (Single Program, Multiple Data) architectures same program is run on each processor but with different inputs Expected operations to support are fixed – but with lots of variants DxT- 7 BLAS3# of Variants Level 3 Basic Linear Algebra Subprograms (BLAS3) basically matrix-matrix operations

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Distributed DLA Kernels Deals with SIMD (Single Instruction, multiple data) architectures same program is run on each processor but with different inputs Expected operations to support are fixed – but with lots of variants DxT- 8 BLAS3# of Variants Gemm Hemm Her2k Herk Symm Syr2k Trmm Trsm triangular matrix-matrix multiply general matrix-matrix multiply Hermitian matrix-matrix multiply symmetric matrix-matrix multiply solving non-singular triangular system of eqns

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Distributed DLA Kernels Deals with SIMD (Single Instruction, multiple data) architectures same program is run on each processor but with different inputs Expected operations to support are fixed – but with lots of variants DxT- 9 BLAS3# of Variants Gemm12 Hemm8 Her2k4 Herk4 Symm8 Syr2k4 Trmm16 Trsm16 triangular matrix-matrix multiply general matrix-matrix multiply Hermitian matrix-matrix multiply symmetric matrix-matrix multiply solving non-singular triangular system of eqns

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12 Variants of Distributed Gemm DxT- 10

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Further Want to optimize “LAPACK-level” algorithms which call DLA and BLAS3 operations: solvers decomposition functions (e.g. Cholesky factorization) eigenvalue problems Have to generate high-performance algorithms for these operations too Our work mechanizes the decisions of experts on van de Geijn’s FLAME project, in particular Elemental library (J. Poulson) rests on 20 years of polishing, creating elegant layered designs of DLA libraries and their computations DxT- 11

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Performance Results Target machines: Benchmarked against ScaLAPACK vendors standard option for distributed memory machines; auto-tuned or manually-tuned only alternative available for target machines except for FLAME DxT automatically generated & optimized BLAS3 and Cholesky FLAME algorithms DxT- 12 Machine# of CoresPeak Performance Argonne’s BlueGene/P (Intrepid)8, TFLOPS Texas Advanced Computing Center (Lonestar) TFLOPS

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DxT- 13

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Cholesky Factorization DxT- 14

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DxT Not Limited to DLA DLA components are stateless – DxT does not require stateless components DxT originally developed for stateful Crash-Fault-Tolerant Servers Correct by Construction, can design high performing programs, and best of all: can teach it to undergrads! Gave project to an undergraduate class of 30+ students Had them build Gamma – classical parallel join algorithm circa 1990s using same DxT techniques we used for DLA code generation We asked them to compare this with “big bang” approach which directly implements the spaghetti diagram (final design) DxT- 15

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Compared to “Big Bang” Preliminary User Study #s DxT /28 = 89%

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They Really Loved It DxT- 17 I have learned the most from this project than any other CS project I have ever done. Honestly, I don't believe that software engineers ever have a source (to provide a DxT explanation) in real life. If there was such a thing we would lose our jobs, because there is an explanation which even a monkey can implement. It's so much easier to implement (using DxT). The big-bang makes it easy to make so many errors, because you can't test each section separately. DxT might take a bit longer, but saves you so much time debugging, and is a more natural way to build things. You won't get lost in your design trying to do too many things at once. I even made my OS group do DxT implementation on the last 2 projects due to my experience implementing gamma.

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What are Secrets Behind DxT? DxT- 18

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