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- Marc Gengler, Matthieu Martel
- PEPM
- 1997

In this paper, we are interested in self-applicable partial evaluation for the pi-calculus, a language which models the concurrent behavior of communicating processes. We use the classic three-steps methodology. First, we write a meta-interpreter for the language. Second, we introduce an abstract analysis that determines which operations (communications)… (More)

- Matthieu Martel
- ESOP
- 2002

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)

Starting with our work on the characterization of the imprecision error in programs using floating-point-numbers, by abstract interpretation, this paper shows that there are numerous perspectives, if one wants to fully qualify the numerical quality of control systems, as found in the aeronautical and automotive industry, for instance. Some very common… (More)

- Matthieu Martel
- SAS
- 2007

Floating-point arithmetic is an important source of errors in programs because of the loss of precision arising during a computation. Unfortunately, this arithmetic is not intuitive (e.g. many elementary operations are not associative, inversible, etc.) making the debugging phase very difficult and empiric. This article introduces a new kind of program… (More)

- Matthieu Martel
- SAS
- 2002

- Arnault Ioualalen, Matthieu Martel
- SAS
- 2012

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)

- Eric Goubault, Matthieu Martel, Sylvie Putot
- ESOP
- 2002

- Sylvie Putot, Eric Goubault, Matthieu Martel
- Numerical Software with Result Verification
- 2003

- Matthieu Martel
- Higher-Order and Symbolic Computation
- 2006

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)