I found this by accident because I wanted to speed up a part on my Pebble watch face, I didn't even know the history of past attempts. The floor variant was born out of a particular rounding optimisation attempt that felt like it could be easier if I just use floor/ceil and moved it into a large int-multiplication space. (this is very tempting because certain constants for rendering and angle calculations are based around large integer constants on that platform, kinda doing half the work towards this idea by creating this particular constraint)