| 1. |
- Eriksson, Oscar, et al.
(författare)
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Partial Evaluation of Automatic Differentiation for Differential-Algebraic Equations Solvers
- 2023
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Ingår i: GPCE 2023 - Proceedings of the 22nd ACM SIGPLAN International Conference on Generative Programming: Concepts and Experiences, Co-located with: SPLASH 2023. - : Association for Computing Machinery (ACM). ; , s. 57-71
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Konferensbidrag (refereegranskat)abstract
- Differential-Algebraic Equations (DAEs) are the foundation of high-level equation-based languages for modeling physical dynamical systems. Simulating models in such languages requires a transformation known as index reduction that involves differentiating individual equations before numerical integration. Commercial and open-source implementations typically perform index reduction by symbolic differentiation (SD) and produce a Jacobian callback function with forward-mode automatic differentiation (AD). The former results in efficient runtime code, and the latter is asymptotically efficient in both runtime and code size. However, AD introduces runtime overhead caused by a non-standard representation of real numbers, and SD is not always applicable in models with general recursion. This work proposes a new approach that uses partial evaluation of AD in the context of numerical DAE solving to combine the strengths of the two differentiation methods while mitigating their weaknesses. Moreover, our approach selectively specializes partial derivatives of the Jacobian by exploiting structural knowledge while respecting a user-defined bound on the code size. Our evaluation shows that the new method both enables expressive modeling from AD and retains the efficiency of SD for many practical applications.
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| 2. |
- Palmkvist, Viktor, et al.
(författare)
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Statically Resolvable Ambiguity
- 2023
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Ingår i: Proceedings of the ACM on Programming Languages. - : ACM Digital Library. - 2475-1421. ; 7:POPL, s. 1686-1712
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Tidskriftsartikel (refereegranskat)abstract
- Traditionally, a grammar defining the syntax of a programming language is typically both context free and unambiguous. However, recent work suggests that an attractive alternative is to use ambiguous grammars,thus postponing the task of resolving the ambiguity to the end user. If all programs accepted by an ambiguous grammar can be rewritten unambiguously, then the parser for the grammar is said to be resolvably ambiguous. Guaranteeing resolvable ambiguity statically---for all programs---is hard, where previous work only solves it partially using techniques based on property-based testing. In this paper, we present the first efficient, practical, and proven correct solution to the statically resolvable ambiguity problem. Our approach introduces several key ideas, including splittable productions, operator sequences, and the concept of a grouper that works in tandem with a standard parser. We prove static resolvability using a Coq mechanization and demonstrate its efficiency and practical applicability by implementing and integrating resolvable ambiguity into an essential part of the standard OCaml parser.
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