Abstract: Innovations in range asymmetric number system (“RANS”) coding and decoding are described herein. Some of the innovations relate to hardware implementations of RANS decoding that organize operations in two phases, which can improve the computational efficiency of RANS decoding. Other innovations relate to adapting RANS encoding/decoding for different distributions or patterns of values for symbols. For example, RANS encoding/decoding can adapt by switching a default symbol width (the number of bits per symbol), adjusting symbol width on a fragment-by-fragment basis for different fragments of symbols, switching between different static probability models on a fragment-by-fragment basis for different fragments of symbols, and/or selectively flushing (or retaining) the state of a RANS decoder on a fragment-by-fragment basis for different fragments of symbols. In many cases, such innovations can improve compression efficiency while also providing computationally efficient performance.