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.CCS Concepts • Software and its engineering → Software design engineering;
No abstract
The problem of producing portable high-performance computing (HPC) software that is cheap to develop and maintain is called the P3 (performance, portability, productivity) problem. Good solutions to the P3 problem have been achieved when the performance profiles of the target machines have been similar. The variety of HPC architectures is, however, large and can be expected to grow larger. Software for HPC therefore needs to be highly adaptable, and there is a pressing need to provide developers with tools to produce software that can target machines with vastly different profiles. Multi-dimensional array manipulation constitutes a core component of numerous numerical methods, such as finite difference solvers of Partial Differential Equations (PDEs). The efficiency of these computations is tightly connected to traversing and distributing array data in a hardware-friendly way. The Mathematics of Arrays (MoA) allows for formally reasoning about array computations and enables systematic transformations of array-based programs, e.g., to use data layouts that fit to a specific architecture. This paper presents a programming methodology aimed for tackling the P3 problem in domains that are well-explored using Magnolia, a language designed to embody generic programming. The Magnolia programmer can restrict the semantic properties of abstract generic types and operations by defining so-called axioms. Axioms can be used to produce tests for concrete implementations of specifications, for formal verification, or to perform semantics-preserving program transformations. We leverage Magnolia's semantic specification facilities to extend the Magnolia compiler with a term rewriting system. We implement MoA's transformation rules in Magnolia, and demonstrate through a case study on a finite difference solver of PDEs how our rewriting system allows exploring the space of possible optimizations.
Context Generic programming, as defined by Stepanov, is a methodology for writing efficient and reusable algorithms by considering only the required properties of their underlying data types and operations. Generic programming has proven to be an effective means of constructing libraries of reusable software components in languages that support it. Generics-related language design choices play a major role in how conducive generic programming is in practice. Inquiry Several mainstream programming languages (e.g. Java and C ++ ) were first created without generics; features to support generic programming were added later, gradually. Much of the existing literature on supporting generic programming focuses thus on retrofitting generic programming into existing languages and identifying related implementation challenges. Is the programming experience significantly better, or different when programming with a language designed for generic programming without limitations from prior language design choices? Approach We examine Magnolia, a language designed to embody generic programming. Magnolia is representative of an approach to language design rooted in algebraic specifications. We repeat a well-known experiment, where we put Magnolia's generic programming facilities under scrutiny by implementing a subset of the Boost Graph Library, and reflect on our development experience. Knowledge We discover that the idioms identified as key features for supporting Stepanov-style generic programming in the previous studies and work on the topic do not tell a full story. We clarify which of them are more of a means to an end, rather than fundamental features for supporting generic programming. Based on the development experience with Magnolia, we identify variadics as an additional key feature for generic programming and point out limitations and challenges of genericity by property. Grounding Our work uses a well-known framework for evaluating the generic programming facilities of a language from the literature to evaluate the algebraic approach through Magnolia, and we draw comparisons with well-known programming languages. Importance This work gives a fresh perspective on generic programming, and clarifies what are fundamental language properties and their trade-offs when considering supporting Stepanov-style generic programming. The understanding of how to set the ground for generic programming will inform future language design. ACM CCS 2012Software and its engineering → Very high level languages;
Conformance checking is an important aspect of process mining that identifies the differences between the behaviors recorded in a log and those exhibited by an associated process model. Machine learning and deep learning methods perform extremely well in sequence analysis. We successfully apply both a Recurrent Neural Network and a Random Forest classifiers to the problem of evaluating whether the alignment cost of a log trace to a process model is below an arbitrary threshold, and provide a lower bound for the fitness of the process model based on the classification.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.