The "invalid number" test should probably be a little more picky:

 ... unless $yearfield =~ /^\d{4}$/;
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or maybe the user should be indulged when entering strings like "02", "99", etc, which entails something messier, like:

 ... unless $yearfield =~ /^(\d{2}){1,2}$/;
 if (length($yearfield) == 2) {
   $millen = ( $yearfield =~ /^0/ ) ? "20" : "19";
   $yearfield = $millen . $yearfield;
 }
 ...
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(In this case, naturally, one shouldn't expect this script to still be in use after 2009, nor should users ever want to refer to years in the 19th century -- I have no problem with that.)