A tutorial on the range variant of asymmetric numeral systems

This paper is intended to be an accessible introduction to the range variant of Asymmetric Numeral Systems (rANS). This version of ANS can be used as a drop in replacement for traditional arithmetic coding (AC). Implementing rANS is more straightforward than AC, and this paper includes pseudo-code which could be converted without too much effort into a working implementation. An example implementation, based on this tutorial, is available at https://raw.githubusercontent.com/j-towns/ans-notes/master/rans.py. After reading (and understanding) this tutorial, the reader should understand how rANS works, and be able to implement it and prove that it attains a near optimal compression rate.