  Optimization Modulo Theories (OMT) is an important extension of SMT which
allows for finding models that optimize given objective functions, typically
consisting in linear-arithmetic or pseudo-Boolean terms. However, many SMT and
OMT applications, in particular from SW and HW verification, require handling
bit-precise representations of numbers, which in SMT are handled by means of
the theory of Bit-Vectors (BV) for the integers and that of Floating-Point
Numbers (FP) for the reals respectively. Whereas an approach for OMT with
(unsigned) BV has been proposed by Nadel & Ryvchin, unfortunately we are not
aware of any existing approach for OMT with FP. In this paper we fill this gap.
We present a novel OMT approach, based on the novel concept of attractor and
dynamic attractor, which extends the work of Nadel & Ryvchin to signed BV and,
most importantly, to FP. We have implemented some OMT(BV) and OMT(FP)
procedures on top of OptiMathSAT and tested the latter ones on modified
problems from the SMT-LIB repository. The empirical results support the
validity and feasibility of the novel approach.
