research-article

Finite difference methods fengshui: alignment through a mathematics of arrays

Authors:

Benjamin Chetioui,

Magne Haveraaen,

Sandra MaciàAuthors Info & Claims

ARRAY 2019: Proceedings of the 6th ACM SIGPLAN International Workshop on Libraries, Languages and Compilers for Array Programming

Pages 2 - 13

https://doi.org/10.1145/3315454.3329954

Published: 08 June 2019 Publication History

Abstract

Numerous scientific-computational domains make use of array data. The core computing of the numerical methods and the algorithms involved is related to multi-dimensional array manipulation. Memory layout and the access patterns of that data are crucial to the optimal performance of the array-based computations. As we move towards exascale computing, writing portable code for efficient data parallel computations is increasingly requiring an abstract productive working environment. To that end, we present the design of a framework for optimizing scientific array-based computations, building a case study for a Partial Differential Equations solver. By embedding the Mathematics of Arrays formalism in the Magnolia programming language, we assemble a software stack capable of abstracting the continuous high-level application layer from the discrete formulation of the collective array-based numerical methods and algorithms and the final detailed low-level code. The case study lays the groundwork for achieving optimized memory layout and efficient computations while preserving a stable abstraction layer independent of underlying algorithms and changes in the architecture.

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Cited By

Grout IMullin L(2023)Mathematics of Arrays Computations for Embedded Systems Applications2023 International Conference on Power, Energy and Innovations (ICPEI)10.1109/ICPEI58931.2023.10473792(1-4)Online publication date: 18-Oct-2023
https://doi.org/10.1109/ICPEI58931.2023.10473792
Grout IMullin L(2022)Realizing Mathematics of Arrays Operations as Custom Architecture Hardware-Software Co-Design SolutionsInformation10.3390/info1311052813:11(528)Online publication date: 4-Nov-2022
https://doi.org/10.3390/info13110528
Chetioui BLarnøy MJärvi JHaveraaen MMullin L(2022)P3 problem and Magnolia language: Specializing array computations for emerging architecturesFrontiers in Computer Science10.3389/fcomp.2022.9313124Online publication date: 31-Oct-2022
https://doi.org/10.3389/fcomp.2022.931312
Show More Cited By

Index Terms

Finite difference methods fengshui: alignment through a mathematics of arrays
1. Software and its engineering
  1. Software creation and management
    1. Designing software
      1. Software design engineering

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cover image ACM Conferences

ARRAY 2019: Proceedings of the 6th ACM SIGPLAN International Workshop on Libraries, Languages and Compilers for Array Programming

June 2019

104 pages

ISBN:9781450367172

DOI:10.1145/3315454

General Chair:
Jeremy Gibbons

Copyright © 2019 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 08 June 2019

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PLDI '19: 40th ACM SIGPLAN Conference on Programming Language Design and Implementation

June 22, 2019

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Overall Acceptance Rate 17 of 25 submissions, 68%

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Cited By

Grout IMullin L(2023)Mathematics of Arrays Computations for Embedded Systems Applications2023 International Conference on Power, Energy and Innovations (ICPEI)10.1109/ICPEI58931.2023.10473792(1-4)Online publication date: 18-Oct-2023
https://doi.org/10.1109/ICPEI58931.2023.10473792
Grout IMullin L(2022)Realizing Mathematics of Arrays Operations as Custom Architecture Hardware-Software Co-Design SolutionsInformation10.3390/info1311052813:11(528)Online publication date: 4-Nov-2022
https://doi.org/10.3390/info13110528
Chetioui BLarnøy MJärvi JHaveraaen MMullin L(2022)P3 problem and Magnolia language: Specializing array computations for emerging architecturesFrontiers in Computer Science10.3389/fcomp.2022.9313124Online publication date: 31-Oct-2022
https://doi.org/10.3389/fcomp.2022.931312
Chetioui BAbusdal OHaveraaen MJärvi JMullin LLow TGibbons J(2021)Padding in the mathematics of arraysProceedings of the 7th ACM SIGPLAN International Workshop on Libraries, Languages and Compilers for Array Programming10.1145/3460944.3464311(15-26)Online publication date: 17-Jun-2021
https://dl.acm.org/doi/10.1145/3460944.3464311

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