Julia Evansfloating point representation
Dr. Juande Santander-Vela@b0rk what about denormalized floats? Do you have a visualization for them? I’d say that they represent even more numbers around the 0.0…
@juandesant i might make one later! Have you ever needed to know about denormalized floats? I'm trying to figure out whether explaining it is worthwhile or whether it's more of an edge case that almost nobody ever runs into.
@b0rk I think is something worth knowing about if you really need to manage calculation precision in floating point.
I learned about them for the first time reading about the SANE (Standard Apple Numeric Environment) in the Turbo Pascal for the Macintosh 1.0 manual… circa 1990!
Taylor R Campbell@b0rk @juandesant Subnormals are very important! For example, fl(x - y) = 0 implies x = y (exactly!) if you have subnormals, and if y/2 < x < 2y then fl(x - y) = x - y (no rounding!).
But if you _don't_ have subnormals, you can't reason like this.
The diagram for subnormals is very simple: zoom in to the smallest and second-smallest exponent, and copy the same resolution between [2^emin, 2^{emin + 1}) into [0, 2^{emin}). Without subnormals, there's a huge gap between 0 and 2^{emin}!