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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Vydáno v:	International journal of computer mathematics Ročník 30; číslo 3-4; s. 165 - 190
Hlavní autor:	Granger, Philippe
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Abingdon Gordon and Breach Science Publishers 01.01.1989 Taylor and Francis
Témata:	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
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Popis
Shrnutí:	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