  Verification of numerical accuracy properties in modern software remains an
important and challenging task. This paper describes an original framework
combining different solutions for numerical accuracy. First, we extend an
existing runtime verification tool called E-ACSL with rational numbers to
monitor accuracy properties at runtime. Second, we present an abstract
compiler, FLDCompiler, that performs a source-to-source transformation such
that the execution of the resulting program, called an abstract execution, is
an abstract interpretation of the initial program. Third, we propose an
instrumentation library FLDLib that formally propagates accuracy properties
along an abstract execution. While each of these solutions has its own
interest, we emphasize the benefits of their combination for an industrial
setting. Initial experiments show that the proposed technique can efficiently
and soundly analyze the accuracy of industrial programs by restricting the
analysis on thin numerical scenarios.
