Abstract
The majority of numerical algorithms employs floating-point vector and matrix operations. On a parallel computer these algorithms should be solved fastand reliably in order to avoid a time-consuming error analysis. The XSC-languages (high-level language extensions for eXtended Scientific Computation) are well-suited for this purpose since they support the design of numerical algorithms delivering correct and automatically verified results. This goal is attained by an arithmetic with maximum accuracy (especially for vector and matrix operations), highly accurate standard functions, and exact evaluation of dot product expressions. Within theESPRIT Parallel Computing Action, one XSC-language, PASCAL-XSC, was implemented on a Supercluster Transputer System under the operating system HELIOS. Parallel algorithms for computationally intensive and maximally accurate matrix operations were implemented and tested on various transputer architectures. We will sketch some features of these architectures and present some benchmarks for the algorithms used. These algorithms form a parallel C runtime library of PASCAL-XSC (or any other XSC-language that uses a C runtime library) and are called automatically. This can be considered a basis for implicit parallelization in an XSC-language.
Zusammenfassung
Die meisten numerischen Algorithmen verwenden Gleitpunktoperationen für Matrizen und Vektoren. Auf Parallelrechnern sollten solche Algorithmen schnellund zuverlässig durchgeführt werden, um zeitaufwendige Fehleranalysen zu vermeiden. Die XSC-Sprachen (Spracherweiterungen für erweitertes wissenschaftliches Rechnen, englisch: eXtendedScientificComputation) sind für diesen Zweck gut geeignet, da sie den Entwurf numerischer Algorithmen unterstützen, die korrekte und automatisch verifizierte Ergebnisse liefern. Dieses Ziel wird durch eine Arithmetik mit maximaler Genauigkeit (insbesondere für Vektor- und Matrixoperationen), hochgenaue Standardfunktionen und exakte Auswertung von Skalarproduktausdrücken erreicht. Innerhalb derESPRIT Parallel Computing Action wurde eine XSC-Sprache, PASCAL-XSC, auf einem Supercluster Transputer System unter dem Betriebs-system HELIOS implementiert. Parallele Algorithmen für rechenintensive und maximal genaue Matrix-operationen wurden auf verschiedenen Transputerarchitekturen implementiert und getestet. Wir werden einige Merkmale dieser Architekturen kurz beschreiben und einige Benchmarks für die verwendeten Algorithmen angeben. Diese Algorithmen bilden eine parallele C Laufzeitbibliothek für PASCAL-XSC (oder irgend eine andere XSC-Sprache, die eine C-Laufzeitbibliothek benutzt) und werden automatisch aufgerufen. Dies kann als Grundstock für eine implizite Parallelisierung in einer XSC-Sprache angesehen werden.
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This work was supported by DFG and ESPRIT Parallel Computing Action.
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Bohlender, G., Kersten, T. & Trier, R. Implicit matrix multiplication with maximum accuracy on various transputer networks. Computing 53, 259–276 (1994). https://doi.org/10.1007/BF02307378
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DOI: https://doi.org/10.1007/BF02307378