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Analysis of modular arithmetic
2007
ACM Transactions on Programming Languages and Systems
We consider integer arithmetic modulo a power of 2 as provided by mainstream programming languages like Java or standard implementations of C. The difficulty here is that the ring Zm of integers modulo m = 2 w , w > 1, has zero divisors and thus cannot be embedded into a field. Not withstanding that, we present intra-and inter-procedural algorithms for inferring for every program point u, affine relations between program variables valid at u. Our algorithms are not only sound but also complete
doi:10.1145/1275497.1275504
fatcat:e4tv4aufdvcj5ar2a65ywmiwg4