We speculate on computational aspects of certain discontinuous functions by taking the Gau\ss{}ian function $[x]$ as a typical example. An algorithm how to compute $[x]$ for a single computable real number is first described, followed by a remark that $[x]$ does {\em not} necessarily preserve sequential computability. Second, $[x]$ is studied in the light of the notions of {\em upper semi-computability} and of {\em limiting computation}. Then two \fr spaces, \inttoreal and \elreal, in which some discontinuous functions will become computable, will be taken up.