There are three algorithms discussed. 1. "Wu-style" circle anti-aliased algorithm. Source. Demo. 2. "Linear-constraint" circle algoritm. Source. Demo. 3. Implicit curve anti-aliased algorithm. Draft. Source. Concept-Demo. The first algorithm uses sqrt function either to precalculate fractions of sqrt or to calculate sqrt when calculating intensities of the pixels. Here are the legacy pages The second and third algorithms do not use sqrt function and any of float or double precision operations. Only integers are used.