#!perl -l

use strict;
use warnings;
use constant PI    => 4 * atan2(1,1);
use constant DPI   => 1e-7;

my @y = (5..15);

foreach my $y (@y) {
    my $f1 = F(PI,$y);
    my $f2 = F(PI+DPI,$y);
    my $delta = $f2 - $f1;
    printf "y=%-2d  delta=%g\n", $y, $delta;
}

# F = pi ^ y
sub F {
    my ($pi, $y) = @_; 
    return $pi ** $y,
}

__END__
y=5   delta=4.87045e-05
y=6   delta=0.000183612
y=7   delta=0.000672972
y=8   delta=0.00241623
y=9   delta=0.00853968
y=10  delta=0.0298091
y=11  delta=0.103013
y=12  delta=0.353045
y=13  delta=1.20155
y=14  delta=4.06515
y=15  delta=13.6833