N + r*N + r*r*N + r*r*r*N
    = (N + r*N + r*r*N + r*r*r*N)*(1-r)/(1-r)
    = (N + (r*N-r*N) + (r*r*N-r*r*N) + (r*r*r*N-r*r*r*N) + ...)/(1-r)
    = N/(1-r)

##</code><code>##

my $max_size = 0;
my $size = 0;
my $recopies = 0;
my $last_pow = 1;

while (++$size) {
  if ($size >= $max_size) {
    use integer;
    my $old_size = $size - 1;
    $max_size = $size + $old_size/5;
    $recopies += $old_size;
  }
  if (not $size%2 and ($size>>1) == $last_pow) {
    my $avg = $recopies/$size;
    printf("% 8d: % 9d recopies.  Avg %1.5f per element\n",
      $size, $recopies, $avg);
    $last_pow = $last_pow + $last_pow;
  }
}

##</code><code>##

       2:         1 recopies.  Avg 0.50000 per element
       4:         6 recopies.  Avg 1.50000 per element
       8:        28 recopies.  Avg 3.50000 per element
      16:        81 recopies.  Avg 5.06250 per element
      32:       195 recopies.  Avg 6.09375 per element
      64:       390 recopies.  Avg 6.09375 per element
     128:       783 recopies.  Avg 6.11719 per element
     256:      1332 recopies.  Avg 5.20312 per element
     512:      2726 recopies.  Avg 5.32422 per element
    1024:      5605 recopies.  Avg 5.47363 per element
    2048:     11566 recopies.  Avg 5.64746 per element
    4096:     23916 recopies.  Avg 5.83887 per element
    8192:     41278 recopies.  Avg 5.03882 per element
   16384:     85513 recopies.  Avg 5.21930 per element
   32768:    177228 recopies.  Avg 5.40857 per element
   65536:    367397 recopies.  Avg 5.60603 per element
  131072:    761722 recopies.  Avg 5.81148 per element
  262144:   1316176 recopies.  Avg 5.02081 per element
  524288:   2729094 recopies.  Avg 5.20533 per element
 1048576:   5658908 recopies.  Avg 5.39676 per element
 2097152:  11734158 recopies.  Avg 5.59528 per element
 4194304:  24331784 recopies.  Avg 5.80115 per element
 8388608:  42045207 recopies.  Avg 5.01218 per element