Information schema question

If I want to get, for example, all of the "user-defined" functions that
are available for execution by the current user, how could I go about
that? I see how to grab these for any given schema, but how can I tell
what schemas the current user has access to if the user can execute the
function? I thought I could use the routine_privileges view, but it
doesn't seem to have functions that I create in it--do I have to
explicitely grant execute on all functions for them to show up in
routine_privileges?

Thanks,
Sean