Introduction to the IEEE 1788-2015 Standard for Interval Arithmetic

Interval arithmetic is a tool of choice for numerical software verification, as every result computed using this arithmetic is self-verified: every result is an interval that is guaranteed to contain the exact numerical values, regardless of uncertainty or roundoff errors. From 2008 to 2015, interval arithmetic underwent a standardization effort, resulting in the IEEE 1788-2015 standard. The main features of this standard are developed: the structure into levels, from the mathematic model to the implementation on computers; the possibility to accommodate different mathematical models, called flavors; the decoration system that keeps track of relevant events during the course of a calculation; the exact dot product for point (as opposed to interval)