The modulo interval: a simple and practical representation for program analysis

In this paper, the modulo interval, an extension of the traditional interval on real numbers, and its useful mathematical properties are presented as a representation for program analysis. Only with two additional parameters to the interval on real numbers, namely the modulus and the residue, the modulo interval can represent information on programs having cyclicity such as loop indices, array subscripts etc., at reasonable complexity and more accuracy. Well-defined arithmetic and set operations on the modulo interval make implementation of compilers simple and reliable. Moreover, application of the modulo interval to program analysis for parallelizing compilers is discussed in this paper