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The tensor algebra compiler
2017
Proceedings of the ACM on Programming Languages
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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)
2001
International Journal of Modern Physics A
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2001 accepted arXiv:math-ph/0006026v2 fatcat:xmk7ym42zfdphpf7bna5up42tmOther Versions
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]
2022
pre-print
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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]
2021
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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]
2021
arXiv
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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]
2018
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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
2018
SIAM Journal on Scientific Computing
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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
1998
Concurrency Practice and Experience
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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
1998
Concurrency Practice and Experience
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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]
2021
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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]
2017
arXiv
pre-print
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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]
2018
arXiv
pre-print
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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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