The only thing that you did not consider is that x*x < x for x < 1. That's why your code doesn't work for input < 1.

Apart from that a couple of small comments concerning your code.

• Don't use prototypes for your subroutines unless you know exactly what you are doing.
• Don't use the variables $a and $b, they are special and used for sort.
• Instead of writing my ($x, $y, $z) = (shift, shift, shift); simply write my ($x, $y, $z) = @_;.