Good rotations (Q1275183)

The paper present a method to find pairs of representable real numbers \(s\) and \(c\) such that \(c^2+s^2\) is as close to 1 as possible. This study is motivated by the undesirable roundoff in the representation of the sine and cosine of an arbitrary angle in a computer. A drastic decrease of the systematic error is obtained, which is negligible compared to the random error of other operations. This approach is applied in celestical mechanics integration with good results.