Nice. Here's a way using select(), so that there's no need for non-core modules (ie. Time::Hires):

use strict;
use warnings;

my $fudgefactor = 0.01;

while (1) {
  my $nextsecond = int time + 1;
  select(undef, undef, undef, $nextsecond - time - $fudgefactor);
  1 while time < $nextsecond;
  printf "%.6f\n", time;
}
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Output:

1579973997.000000
1579973998.000000
1579973999.000000
1579974000.000000
1579974001.000000
^C
[download]