I'd like an alorithm for converting to and from the epoch time, that I
can use in an UNIX shell script.

I assume that you mean that you have seconds since the epoch.  But
what is the format you want to convert it to?  Or what format do  you
want to convert to seconds since the epoch?

I can tell you that probably anything you want to do is possible
through the date command and a little arithmetic.  Give me an example
and I can show you how to do it.