Static analysis of arithmetical congruences

In this paper, a new kind of static (or semantic) analysis is defined: congruence analysis, which is conceived to discover the properties of the following type: "the integer valued variable X is congruent to c modulo m", where c and m are automatically determined integers. This analysis is...

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Bibliographic Details
Published in:International journal of computer mathematics Vol. 30; no. 3-4; pp. 165 - 190
Main Author: Granger, Philippe
Format: Journal Article
Language:English
Published: Abingdon Gordon and Breach Science Publishers 01.01.1989
Taylor and Francis
Subjects:
Abstract interpretation
Applied sciences
automatic vectorization
Computer science; control theory; systems
D.1.2 [Programming Techniques]: Automatic Programming
D.3.4 [Processors]: Optimization
Exact sciences and technology
F.3.1 [Specifying and Verifying and Reasoning about Programs]: Invariants, Mechanical Verification
F.3.2. [Semantics of Programming Languages]: Operational Semantics
Programming theory
semantic analysis
Theoretical computing
ISSN:0020-7160, 1029-0265
Online Access:Get full text
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Summary:In this paper, a new kind of static (or semantic) analysis is defined: congruence analysis, which is conceived to discover the properties of the following type: "the integer valued variable X is congruent to c modulo m", where c and m are automatically determined integers. This analysis is then related to an algebraic framework and wholly characterized. Moreover, we show an example how it can be useful for automatic vectorization. Finally, we present some extensions of it, namely its combination with the analysis of bounds, and also some analyses defined when the modulus of congruences is given a priori.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207168908803778