I think the atan2+sincos version is more readable, so I guess we actually do agree there. But I wouldn’t (and didn’t) use that in a game engine. For rounding an

I think the atan2+sincos version is more readable, so I guess we actually do agree there. But I wouldn’t (and didn’t) use that in a game engine. For rounding and readability in a real engine, I’d name 4 of the 8 directions and look for the largest absolute value dot product. That would at least corral the constants. And I’d use (did use) f16 or integer arithmetic. One reason I have to support this kind of optimization and not reach for the trig method by default is the last time I wrote a controller system, it wasn’t limited to something as small as deciding on a single dpad-like direction, it was a much larger system that designers could author controller recognizers for, up to and including drawing shapes like a circle with the stick, or entering a time based sequence of inputs (think Contra’s famous up-down-up-down-etc-etc cheat code). If you have sequences and multiple players and high frame rate and many possible patterns to identify, that’s when efficiency of these small operations really starts to add up. I actually spent the most development time ensuring that the amount of time spent not recognizing controls was minimized, making sure that a no-op pass through the system was measured in nanoseconds and not microseconds.