Making a scatter plot of 400_000 data points, some of the plots had odd gaps in coverage. It took me a little while to realize that it was only when the data was farther from the origin — it was the raw bfloat16 precision. Everything looks great from -1 to 1, but as you go past 2 and 4, the coverage gaps get larger. My intuition didn't have it being quite so "discretely countable" at those modest numeric values. Float32 for comparison.

→ View original post on X — @id_aa_carmack, 2026-04-09 23:01 UTC