What would be useful is a method that generates (i.e., a generator in the Python sense) the (continued fraction) convergents to a rational. People wanting specific constraints on a rational approximation (including, but not limited to, the two you identified) can easily build them on top of such a generator. By "useful" I don't mean lots of people will use it ;-) I mean /some/ people will use it -- a way to generate the sequence of convergents is a fundamental tool that can be used for all sorts of stuff, by those with advanced applications.
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