[stephencanon]

It's not much of a "hack", it's literally how the number format works. If you implemented it without the "hack", you'd just be at the mercy of the compiler to see through your arithmetic on the float bit patterns and reconstitute it.

It's not actually that fast, either. Every mainstream architecture from the last 15 years (except maybe RISC-V, since it's exactly the sort of thing they would forget to add) has a "approximate square root" instruction with single-cycle throughput, and they're all both more accurate and more efficient than this. It was good for its time, but it's time has passed.