How do you compute the midpoint of an interval?

Frédéric Goualard (1)

1 LINA - Laboratoire d'Informatique de Nantes Atlantique

The algorithm that computes the midpoint of an interval with floating-point bounds requires some careful devising to correctly handle all possible inputs. We review several implementations from prominent C/C++ interval arithmetic packages and analyze their potential failure to deliver correct results. We then highlight two implementations that avoid common pitfalls. The results presented are also relevant to non-interval arithmetic computation such as the implementation of bisection methods. Enough background on IEEE 754 floating-point arithmetic is provided for this paper to serve as a practical introduction to the analysis of floating-point computation.

Mots clés: rounding error; floating-point number; midpoint; interval arithmetic; IEEE 754 standard

Domaines: Arithmétique des ordinateurs

Frédéric Goualard. How do you compute the midpoint of an interval?. ACM Transactions on Mathematical Software, 2014, 40 (2), ⟨10.1145/2493882⟩. ⟨hal-00576641v2⟩