You really only need to compute one eighth of a circle segment (so, zero to pi/4), everything else you can do by symmetry by switching signs and flipping x, y.

You really only need to compute one eighth of a circle segment (so, zero to pi/4), everything else you can do by symmetry by switching signs and flipping x, y. (And if you supported a larger range, you’d waste precision). In high school I was writing a paint program in BASIC on the Apple ][. Drawing circles was mind-numbingly slow until I read an article somewhere that pointed this out. It was like magic.