Implementing Taylor models arithmetic with floating‐point arithmetic

Abstract The implementation of Taylor models arithmetic may use floating‐point arithmetic to benefit from the speed of the floatingpoint implementation. The issue is then to take into account the roundoff errors. Here, we assume that the floating‐point arithmetic is compliant with the IEEE‐754 standard. We show how to get tight bounds of the roundoff errors, and more generally how to get high accuracy for the coefficients as well as for the bounds on the roundoff errors