Trustworthy numerical computation in Scala

Abstract

Modern computing has adopted the floating point type as a default way to describe computations with real numbers. Thanks to dedicated hardware support, such computations are efficient on modern architectures, even in double precision. However, rigorous reasoning about the resulting programs remains difficult. This is in part due to a large gap between the finite floating point representation and the infinite-precision real-number semantics that serves as the developers' mental model. Because programming languages do not provide support for estimating errors, some computations in practice are performed more and some less precisely than needed.