> As you can see, the technique is so simple that I'd expect that somebody has done this before, but I've looked around and not found it documented anywhere.

I'm one of those people I suppose. Yes, if you want to play with microoptimisations and part of a calculation are known, you can flip a division into a mult (and shift).

This might seem somewhat useless at first, but you can use this to e.g. speed up calculations in nested loops, where you can precompute this for relevant loop-layers.