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The tensor algebra compiler

Fredrik Kjolstad, Shoaib Kamil, Stephen Chou, David Lugato, Saman Amarasinghe
2017 Proceedings of the ACM on Programming Languages  
A compiler for dense and sparse tensor algebra.  ...  Tensor and linear algebra is pervasive in data analytics and the physical sciences. Often the tensors, matrices or even vectors are sparse.  ...  taco: The Tensor Algebra Compiler We have implemented the technique in this paper in a C++ library called taco (short for Tensor Algebra Compiler).  ... 
doi:10.1145/3133901 dblp:journals/pacmpl/KjolstadKCLA17 fatcat:6bkwkjzqg5cxfjceuvtx5454bi

COMPILATION OF RELATIONS FOR THE ANTISYMMETRIC TENSORS DEFINED BY THE LIE ALGEBRA COCYCLES OF su(n)

J. A. DE AZCÁRRAGA, A. J. MACFARLANE
2001 International Journal of Modern Physics A  
This paper attempts to provide a comprehensive compilation of results, many new here, involving the invariant totally antisymmetric tensors (Omega tensors) which define the Lie algebra cohomology cocycles  ...  Since the Omega tensors occur naturally within the algebra of totally antisymmetrised products of λ-matrices of su(n), relations within this algebra are studied in detail, and then employed to provide  ...  One of the authors (JA) wishes to thank the theory group at Imperial College, London, for their hospitality during the last stages of this paper.  ... 
doi:10.1142/s0217751x01003111 fatcat:l3qqthvv35f6fdv23jzxj2oz5y

DISTAL: The Distributed Tensor Algebra Compiler [article]

Rohan Yadav and Alex Aiken and Fredrik Kjolstad
2022 pre-print
We introduce DISTAL, a compiler for dense tensor algebra that targets modern distributed and heterogeneous systems.  ...  DISTAL compiles a tensor algebra domain specific language to a distributed task-based runtime system and supports both nodes with multi-core CPUs and multiple GPUs.  ...  We would like to thank the Legion team, including Mike Bauer, Sean Treichler, Manolis Papadakis, and Wonchan Lee for their feedback and support during the development of DISTAL.  ... 
doi:10.1145/3519939.3523437 arXiv:2203.08069v1 fatcat:4p2puznv3nh4xbkunmkfathdby

A High-Performance Sparse Tensor Algebra Compiler in Multi-Level IR [article]

Ruiqin Tian, Luanzheng Guo, Jiajia Li, Bin Ren, Gokcen Kestor
2021 arXiv   pre-print
Our results show that the performance of automatically generated kernels outperforms the state-of-the-art sparse tensor algebra compiler, with up to 20.92x, 6.39x, and 13.9x performance improvement, for  ...  We propose a tensor algebra domain-specific language (DSL) and compiler infrastructure to automatically generate kernels for mixed sparse-dense tensor algebra operations, named COMET.  ...  RELATED WORK Compiler for Tensor Algebra. Compiler techniques have been used to drive irregular computation in tensor algebra [8, 25, 28, 34, 65] .  ... 
arXiv:2102.05187v1 fatcat:nc5bu7bgobgsxjbppkjtesxmkq

Compiler Support for Sparse Tensor Computations in MLIR [article]

Aart J.C. Bik, Penporn Koanantakool, Tatiana Shpeisman, Nicolas Vasilache, Bixia Zheng, Fredrik Kjolstad
2022 arXiv   pre-print
of the computation.  ...  Therefore, we propose treating sparsity as a property of tensors, not a tedious implementation task, and letting a sparse compiler generate sparse code automatically from a sparsity-agnostic definition  ...  Acknowledgments The authors would like to extend their thanks to the MLIR team, with a special shout-out to Mehdi Amini, Eugene Burmako, Diego Caballero, Albert Cohen, Sanjoy Das, Tobias Gysi, Stephan  ... 
arXiv:2202.04305v1 fatcat:6qijxmernbev7pwmt6lgqdvziy

COMET: A Domain-Specific Compilation of High-Performance Computational Chemistry [article]

Erdal Mutlu, Ruiqin Tian, Bin Ren, Sriram Krishnamoorthy, Roberto Gioiosa, Jacques Pienaar, Gokcen Kestor
2021 arXiv   pre-print
In this paper we present COMET, a domain-specific programming language and compiler infrastructure for tensor contractions targeting heterogeneous accelerators.  ...  Tensor contractions are the fundamental computational building block of these simulations.  ...  RELATED WORK Among the compiler-based approaches for tensor algebra, the Tensor Contraction Engine (TCE) [8] is an early effort as a compiler framework that automatically optimizes dense tensor contractions  ... 
arXiv:2102.06827v1 fatcat:aekbdo7nfrhqfd42llgzbyhh7a

DLVM: A modern compiler infrastructure for deep learning systems [article]

Richard Wei, Lane Schwartz, Vikram Adve
2018 arXiv   pre-print
Designed as a modern compiler infrastructure inspired by LLVM, DLVM is more modular and more generic than existing deep learning compiler frameworks, and supports tensor DSLs with high expressivity.  ...  We present DLVM, a design and implementation of a compiler infrastructure with a linear algebra intermediate representation, algorithmic differentiation by adjoint code generation, domain-specific optimizations  ...  LLVM is a robust and mature compiler infrastructure with multiple back-ends, including NVIDIA GPUs. Many high-level DLVM IR linear algebra instructions over tensors abstract lower-level operations.  ... 
arXiv:1711.03016v5 fatcat:6rh2hyxr6zh4bikxpqf4ar6vee

A Unified Iteration Space Transformation Framework for Sparse and Dense Tensor Algebra [article]

Ryan Senanayake, Fredrik Kjolstad, Changwan Hong, Shoaib Kamil, and Saman Amarasinghe
2019 arXiv   pre-print
We address the problem of optimizing mixed sparse and dense tensor algebra in a compiler.  ...  sparse tensor algebra GPU code.  ...  tensor algebra compilation.  ... 
arXiv:2001.00532v1 fatcat:qdaa7blqmjgctcgyy6ogouod3q

TSFC: A Structure-Preserving Form Compiler

Miklós Homolya, Lawrence Mitchell, Fabio Luporini, David A. Ham
2018 SIAM Journal on Scientific Computing  
This is also achieved in part by a two-stage approach that cleanly separates the lowering of finite element constructs to tensor algebra in the first stage, from the scheduling of those tensor operations  ...  This enables us to preserve the tensor structure of expressions longer through the compilation process than other form compilers.  ...  The authors would like to thank Andrew T. T. McRae for reviewing the manuscript of this paper. The integration of TSFC as an FFC representation was undertaken by Jan Blechta.  ... 
doi:10.1137/17m1130642 fatcat:b37smdhsirhtbdjtahzxcgagoi

Java signal processing: FFTs with bytecodes

John Glossner, Jesse Thilo, Stamatis Vassiliadis
1998 Concurrency Practice and Experience  
Additionally, we h a v e developed a Tensor algebra FFT library in both Matlab and Java. Each of the Tensor libraries has been coded to exploit the characteristics of the source language.  ...  We compare the performance of the Fast Fourier Transform using Java i n terpreters, compilers, and native execution.  ...  Tensor Algebra In this section, we provide an introduction to the Fast Fourier Transform and Tensor algebra.  ... 
doi:10.1002/(sici)1096-9128(199809/11)10:11/13<1173::aid-cpe403>3.0.co;2-1 fatcat:ks5uhv34b5axneqxg6nxnsecta

Java signal processing: FFTs with bytecodes

John Glossner, Jesse Thilo, Stamatis Vassiliadis
1998 Concurrency Practice and Experience  
Additionally, we h a v e developed a Tensor algebra FFT library in both Matlab and Java. Each of the Tensor libraries has been coded to exploit the characteristics of the source language.  ...  We compare the performance of the Fast Fourier Transform using Java i n terpreters, compilers, and native execution.  ...  Tensor Algebra In this section, we provide an introduction to the Fast Fourier Transform and Tensor algebra.  ... 
doi:10.1002/(sici)1096-9128(199809/11)10:11/13<1173::aid-cpe403>3.3.co;2-t fatcat:imjl3ibckvgwxj52zswu3zydmy

Dynamic Sparse Tensor Algebra Compilation [article]

Stephen Chou, Saman Amarasinghe
2021 arXiv   pre-print
the results of sparse tensor algebra computations in dynamic data structures.  ...  This paper shows how to generate efficient tensor algebra code that compute on dynamic sparse tensors, which have sparsity structures that evolve over time.  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the aforementioned funding agencies.  ... 
arXiv:2112.01394v1 fatcat:blwlfyandbdajmrql4r6cabkmy

Really Embedding Domain-Specific Languages into C++ [article]

Hal Finkel, Alexander McCaskey, Tobi Popoola, Dmitry Lyakh, Johannes Doerfert
2020 arXiv   pre-print
In this paper, we describe an extension to the Clang C++ compiler to support syntax plugins, and we demonstrate how this mechanism allows making use of DSLs inside of a C++ code base without needing to  ...  separate the DSL source code from the surrounding C++ code.  ...  These factors make linear algebra a good match for DSLs, and motivated the creation of TACO, the Tensor Algebra Compiler [9] .  ... 
arXiv:2010.08439v1 fatcat:2wgdyya6n5c7jnwt6i24xd4h7a

Tensors Come of Age: Why the AI Revolution will help HPC [article]

John L. Gustafson, Lenore M. Mullin
2017 arXiv   pre-print
This article discusses how the automation of tensor algorithms, based on A Mathematics of Arrays and Psi Calculus, and a new way to represent numbers, Unum Arithmetic, enables mechanically provable, scalable  ...  Why are we seeing convergent evolution to the use of tensor processors, optimized tensor algebras in languages, and nontraditional arithmetic formats?  ...  An algebra exists for index manipulation that can be part of the compiler smarts, freeing the programmer from having to worry about details like "Is this row-major or column-major order?"  ... 
arXiv:1709.09108v1 fatcat:bxl4cc5egfea5jwjfggsyvctji

Compiling Diderot: From Tensor Calculus to C [article]

Charisee Chiw and Gordon L. Kindlmann and John Reppy
2018 arXiv   pre-print
We describe the challenges in compiling a language like Diderot, the design of EIN, and the transformation used by the compiler.  ...  Diderot supports higher-order programming where tensor fields are first-class values and where differential operators and lifted linear-algebra operators can be used to express mathematical reasoning directly  ...  organizations or the U.S.  ... 
arXiv:1802.06504v1 fatcat:nfwsuvl5z5g6nlycm3haxbxyr4
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