[plus]

You are discussing a very different use of the word "reversible". This blog post is discussing mathematical operations on 32-bit integers where the original number can be recovered through an inverse operation. You are talking about the concept of physical reversibility, which refers to processes in which the change in entropy is (close to) zero. The first is a mathematical concept relating to operations over the field of 32-bit integers, while the latter is a physical concept related to second law of thermodynamics. I guarantee that XORing a 32-bit integer with a fixed value is not a thermodynamically reversible process on any known architecture.

[krastanov]

This was my point when I said "far from considering it in practice". An operation has to be (a) logically reversible (thermodynamically reversible in theory, like XOR) before you can make (b) real reversible hardware with it (thermodynamically reversible hardware implementation). Most operations we use in typical hardware are obviously not (b), but they are also not even (a).