$x = $y * 16;
$x = $y << 4; #Much faster
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This is an example (like most) where you can't tell what Perl's going to do. It turns out to only be 12% faster for the example you gave (which I don't consider an order of magnitude). Without "use integer", shift is only about 16% faster. Which I wouldn't have expected, either.

Benchmark: running multiply, shift, each for at least 10 CPU seconds...
  multiply: 12 wallclock secs (10.87 usr +  0.00 sys = 10.87 CPU) @ 798444.43/s (n=8679091)
     shift: 10 wallclock secs (10.57 usr + -0.01 sys = 10.56 CPU) @ 894401.80/s (n=9444883)
             Rate multiply    shift
multiply 798444/s       --     -11%
shift    894402/s      12%       --

use Benchmark;
use integer;
Benchmark::cmpthese(-10, {
 multiply => sub { my $y = 3; my $x = $y * 16 },
 shift => sub { my $y = 3; my $x = $y << 4 } }
);
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