Reversible Radix Sort

Reversible computing is maturing and progressing technically continuously and rapidly, although it is still little studied by the scientific community. Few reversible versions of classical algorithms are known in the literature, due to the lack of knowledge about the reversibility paradigm. However, in times of high demand for high-performance computing, reversibility becomes increasingly relevant due to the vital need to reduce energy consumption to perform computing.
Given that sorting is one of the most common subroutines in any complex project, this article aims to reduce this gap by discussing aspects of Radix Sort reversibility and clarifying the theoretical foundations of algorithm reversibility.
The objective is to explain the mechanics of combining reversible primitives in a concrete context, highlighting how reversibility imposes structural constraints and, simultaneously, suggesting ways to circumvent them.