Evidently you feel more comfortable using degrees rather than radians but the conversion to and from radians<->degrees serves no real purpose. Just define:

my $ninety_degrees = atan(1)*2;
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You will get a division by zero crash in the case where $x and $y = 0 as it will fall through your 'extreme cases'. You can remove the dependency on a module by using radians and using a function for atan() like:

sub atan {
    return 0 if $_[0]==0;
    return $_[0] > 0 ?
         atan2(sqrt(1+$_[0]*$_[0]),sqrt(1+1/($_[0]*$_[0]))) :
        -atan2(sqrt(1+$_[0]*$_[0]),sqrt(1+1/($_[0]*$_[0])));
}
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