>> integral values less than about 2⁵³ will be represented and compared exactly

Since this OT is turning into a C refresher course, factual accuracy should be in order. Your statement is true of C/C++ double, which is also what Perl uses for numeric values. The example  float x, y; declares a couple of single-precision floats, which can represent exactly integral values of up to about 2²⁵.

A summary of IEEE-754 format can be found here and an interactive converter here.

Rudif