This paper is intended to be a brief and accessible introduction to the range variant of asymmetric numeral systems (ANS), a system for lossless compression of sequences which can be used as a drop in replacement for arithmetic coding (AC). Because of the relative simplicity of ANS, we are able to provide enough mathematical detail to rigorously prove that ANS attains a compression rate close to the Shannon limit. Pseudo-code, intuitive interpretation and diagrams are given alongside the mathematical derivations. A working Python demo which accompanies this tutorial is available at https://raw.githubusercontent.com/j-towns/ans-notes/master/rans.py.
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