$number wasn't guaranteed to be a whole number (and I guess that makes % fail)

No, Perl is OK with that:

 3:03 >perl -MData::Dump -wE "my @array; $array[5.35968 % 2] = 42; dd 
+\@array;"
[undef, 42]

 3:03 >
[download]

But the original loop almost certainly wasn’t doing what you thought it was. With an initial value of 192:

 3:03 >perl -wE "my $iterations = 0; my $number = 192; while ($number 
+!= 0) { $number /= 2; ++$iterations; } say qq[$iterations iterations]
+;"
1083 iterations

 3:06 >
[download]

The loop terminates when $number is zero, but (on my Perl, which is 64-bit) this test doesn’t succeed until division by two has reduced $number all the way down to half of 4.94065645841247 × 10^-324 — which is a very small number!

Hope that helps,