Analytic models of machine arithmetic

We present new methods for constructing analytic models of information systems whose requirements are specified by formal theories. The methods are based on a special modification of a model-theoretic approach, called partial interpretation. We construct analytic models of computer implementations of arithmetic–partial interpretations of arithmetic theories with finite universes. We describe the main classes of partial interpretations of integer arithmetics, which are distinguished by the methods for processing overflows. We consider a partial interpretation of the arithmetic of rational numbers based on the IEEE Standard 754. We analyze computation models supported by various programming languages and propose paths for their development.