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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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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Abstract 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.
AbstractList 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.
Author Granger, Philippe
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Cites_doi 10.1145/29873.29875
10.1145/512950.512973
10.1145/512760.512770
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Taylor and Francis
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References Granger P. (CIT0006)
Cousot P. (CIT0002) 1981
CIT0001
Hardy G. H. (CIT0007) 1979
CIT0003
CIT0005
CIT0004
Lang S. (CIT0008) 1984
Stark H. M. (CIT0009) 1970
References_xml – ident: CIT0001
  doi: 10.1145/29873.29875
– volume-title: An Introduction to Number Theory
  year: 1970
  ident: CIT0009
– start-page: 303
  volume-title: Program Flow Analysis: Theory and Applications
  year: 1981
  ident: CIT0002
– ident: CIT0003
  doi: 10.1145/512950.512973
– ident: CIT0004
– volume-title: Rapport de recherche
  ident: CIT0006
– ident: CIT0005
  doi: 10.1145/512760.512770
– volume-title: Algebra
  year: 1984
  ident: CIT0008
– volume-title: An Introduction to the Theory of Numbers
  year: 1979
  ident: CIT0007
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SubjectTerms 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
Title Static analysis of arithmetical congruences
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Volume 30
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