(Video by Bismuth) The world of Super Mario 64 is more or less a 3-dimensional torus \(T^3\). Marios position is stored as a float, but cast down to a short for the collision detection, meaning that only values up between \(-32768\) and \(32767\) are actually detected as different positions for the collision detection. Therefor marios position detection is calculated in \(B:= (\mathbb{R}/65536\mathbb{Z})^3\), and his actual position is calculated in \(P:=(\mathbb{R} / (1.17549435 \times 10^{-38})\mathbb{Z})^3\), here we still need to mod out, because of Nintendo 64 IEEE‑754 floating point arithmetic.
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