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for ( my $c= 0; $c<= $#clk_output; $c++) {
   for ( my $d = 0; $d <= $#{$clk_output[$c]}; $d++ ) {
...
    }
}
print Dumper \@clk_new;

$VAR1 = [ 'ux_prim_clk', 'ux_prim_clk', 'ux_prim_clk',
          'ux_side_clk', 'ux_side_clk', 'ux_side_clk',
          'ux_xtal_frm_refclk', 'ux_xtal_frm_refclk',
          'ux_xtal_frm_refclk', 'ux_xtal_frm_refclk'   ];

for ( my $c= 0; $c<= $#clk_output; $c++) {
    $clk_new = join '_', @{$clk_output[$c]};
    push @clk_new, $clk_new;
}
print Dumper \@clk_new;

$VAR1 = [ 'ux_prim_clk', 'ux_side_clk', 'ux_xtal_frm_refclk' ];

for my $c (@clk_output) {
    $clk_new = join '_', @$c;
    push @clk_new, $clk_new;
}

for my $c (@clk_output) {
    push @clk_new, join '_', @$c;
}

for (@clk_output) {
    push @clk_new, join '_', @$_;
}

@new_list = map { operation_to_perform_on_each_element } @old_list;

@clk_new = map { join '_', @$_ } @clk_output;