[dahart]

Yes of course there’s a more graceful approach. You can use an actual divide instruction or routine instead of the bit-casting subtraction trick.

It’s not about interfaces. The point is that a single subtract is simpler math, and (probably) faster than a divide, and it gets you surprisingly close to the right answer. The reason it works is subtracting two exponents is a subtraction in log space which is equivalent to a divide in linear space.

People don’t use this trick in practice that much if at all, especially these days with GPUs that do reciprocals and square roots in hardware, it’s just an interesting thing to know about that helps solidify our understanding of floating point numbers and logarithms.