I don't think SelfLoader or AutoLoader are really what he wants here. They are designed for situations in which the compilation of code is very expensive, and you don't want to bother unless the code is needed.

In this case, it sounds like the code to populate the constants is relatively simple, and won't take long to compile, it just takes a while to run.

This screams accessor to me.

Instead of making these constants part of your 'public' API, make them internal, and write an accessor for them that initializes them the first time it calls, and returns them everytime after that:

package mypackage;
my $sqrt_2 = undef; # not visible outside of mypackage

sub get_sqrt_2 {
   unless (defined $sqrt_2) {
      # do a bunch of work to set $sqrt_2
   }
   return $sprt_2;
}
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