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PLDI 2021
Sun 20 - Sat 26 June 2021 PLDI
Mon 21 Jun 2021 11:15 - 11:45 at ARRAY - Session 1 (principles) Chair(s): Artjoms Šinkarovs

Multi-dimensional array manipulation constitutes a core component of numerous numerical methods, e.g. finite difference solvers of Partial Differential Equations (PDEs). The efficiency of such computations is tightly connected to traversing array data in a hardware-friendly way. The Mathematics of Arrays (MoA) allows reasoning about array computations at a high level and enables systematic transformations of array-based programs. We have previously shown that stencil computations reduce to MoA’s Denotational Normal Form (DNF). Here we bring to light MoA’s Operational Normal Forms (ONFs) that allow for adapting array computations to hardware characteristics. ONF transformations start from the DNF. Alongside the ONF transformations, we extend MoA with rewriting rules for padding. These new rules allow both a simplification of array indexing and a systematic approach to introducing halos to PDE solvers. Experiments on various architectures confirm the flexibility of the approach.

Mon 21 Jun

Displayed time zone: Eastern Time (US & Canada) change

09:00 - 11:45
Session 1 (principles)ARRAY at ARRAY
Chair(s): Artjoms Šinkarovs Heriot-Watt University, UK
Day opening
Welcome and opening
Jeremy Gibbons Department of Computer Science, University of Oxford
Towards size-dependent types for array programming
Troels Henriksen University of Copenhagen, Denmark, Martin Elsman University of Copenhagen, Denmark
Padding in the Mathematics of Arrays
Benjamin Chetioui University of Bergen, Norway, Ole Abusdal Western Norway University of Applied Sciences, Magne Haveraaen University of Bergen, Norway, Jaakko Järvi University of Turku, Lenore Mullin University at Albany, SUNY