I timed those two functions along with the following:

sub by_string {
  my $n = shift;
  return length(sprintf "%b", $n) - 1;
}
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I tested with high bits using int rand(2**64), medium bits int rand(2**32) and lower bits int rand(2**16) for 1e6 iterations.

log    linear sprintf
0.2917 0.4427 0.3370  avg_sig=62
0.2786 2.8430 0.3056  avg_sig=30
0.2826 4.1060 0.2986  avg_sig=14
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