Correct approximation of IEEE 754 floating-point arithmetic for program verification

Abstract Verification of programs using floating-point arithmetic is challenging on several accounts. One the difficulties reasoning about such due to peculiarities arithmetic: rounding errors, infinities, non-numeric objects (NaNs), signed zeroes, denormal numbers, different modes, etc. possibility reason model a program computation path by means set ternary constraints form "Image missing"and use constraint propagation techniques infer new information variables’ possible values. In this setting, we define and prove correctness algorithms precisely bound value one variables x , y z starting from bounds known for other two. We do each operations mode defined IEEE 754 binary standard, even in case effect only partially known. This first time that so-called filtering are their formally proved. an important slab paving way formal verification arithmetics.