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We introduce a concrete semantics for floating-point operations which describes the propagation of roundoff errors throughout a computation. This semantics is used to assert the correctness of an abstract interpretation which can be straightforwardly derived from it. In our model, every elementary operation introduces a new first order error term, which is(More)
We present a new method for solving the fixed point equations that appear in the static analysis of programs by abstract interpretation. We introduce and analyze a policy iteration algorithm for monotone self-maps of complete lattices. We apply this algorithm to the particular case of lattices arising in the interval abstraction of values of variables. We(More)
Exact computations being in general not tractable for computers , they are approximated by floating-point computations. This is the source of many errors in numerical programs. Because the floating-point arithmetic is not intuitive, these errors are very difficult to detect and to correct by hand and we consider the problem of automatically synthesizing(More)
We introduce a concrete semantics for floating-point operations which describes the propagation of roundoff errors throughout a calculation. This semantics is used to assert the correctness of a static analysis which can be straightforwardly derived from it. In our model, every elementary operation introduces a new first order error term, which is later(More)