Optimal Inverse Projection of Floating-Point Addition

Diane Gallois-Wong (1) , Sylvie Boldo (1) , Pascal Cuoq (2)

1 TOCCATA - Formally Verified Programs, Certified Tools and Numerical Computations
2 TIS - TrustInSoft

In a setting where we have intervals for the values of floating-point variables x, a, and b, we are interested in improving these intervals when the floating-point equality $x ⊕ a = $b holds. This problem is common in constraint propagation, and called the inverse projection of the addition. It also appears in abstract interpretation for the analysis of programs containing IEEE 754 operations. We propose floating-point theorems that provide optimal bounds for all the intervals. Fast loop-free algorithms compute these optimal bounds using only floating-point computations at the target precision.

Domaines: Logique en informatique [cs.LO]; Arithmétique des ordinateurs

Diane Gallois-Wong, Sylvie Boldo, Pascal Cuoq. Optimal Inverse Projection of Floating-Point Addition. Numerical Algorithms, inPress, 83 (3), pp.957--986. ⟨10.1007/s11075-019-00711-z⟩. ⟨hal-01939097⟩