```Arnaud Bergeron wrote:

> I did my own benchmarking and my results are contrary to what was said
> before.

/ ... snip demonstration in which n * n is 3.2 x faster than n ** 2

> It shows that n * n is faster.
>
> However this may be an architecture difference. (for reference I'm on
> a mac, a G3)

Interesting. It seems to be implementation-related after all. On the other
hand, if this and the prior result are averaged, there seems little overall
difference, so for a typical programmer with an arbitrary platform, it
might be a toss-up.

Here are my tests (Linux on an Intel Xeon, clock 3 GHz):

-----------------------------------------

#!/usr/bin/ruby

require 'benchmark'

T=1000000
n = 413

Benchmark.bmbm(10) do |x|
x.report("n * n")  { T.times { n * n } }
x.report("n ** 2") { T.times { n ** 2 } }
end

-----------------------------------------

Result:

Rehearsal ---------------------------------------------
n * n       1.033333   0.000000   1.033333 (  0.615591)
n ** 2      2.083333   0.000000   2.083333 (  1.262649)
------------------------------------ total: 3.116667sec

user     system      total        real
n * n       1.133333   0.000000   1.133333 (  0.686552)
n ** 2      2.283333   0.000000   2.283333 (  1.377575)

In this example (n = 413), n * n is about twice as fast as n ** 2.

But ... if I choose a larger value for n (41398765432), so that the
computation is carried out using Bignum:

Rehearsal ---------------------------------------------
n * n       1.566667   0.016667   1.583333 (  0.953782)
n ** 2      1.633333   0.000000   1.633333 (  0.992337)
------------------------------------ total: 3.216667sec

user     system      total        real
n * n       1.583333   0.000000   1.583333 (  0.954614)
n ** 2      1.650000   0.016667   1.666667 (  1.007131)

A much smaller advantage for n * n when n is a Bignum.

Then, using a much bigger number (413987654321987654321):

Rehearsal ---------------------------------------------
n * n       1.816667   0.000000   1.816667 (  1.095099)
n ** 2      1.866667   0.000000   1.866667 (  1.128506)
------------------------------------ total: 3.683333sec

user     system      total        real
n * n       1.850000   0.016667   1.866667 (  1.139751)
n ** 2      1.850000   0.000000   1.850000 (  1.114387)

In this case, n * n loses its advantage by a slight margin.

Overall, a toss-up.

--
Paul Lutus
http://www.arachnoid.com

```