Class ArctanAsymptote

source code

Arctan asymptote function for mapping (-inf,inf) to [0,1].

With all attributes constant, either the class or an instance can be used.

An asymptote function is monotonically increasing and finite everywhere. Assuming the function is a at -inf and b at +inf, scale is 1/(b-a) and offset is a. Together with an inverse function, this allows us to transform between an infinite range and the range [0,1]. Semidefinite map to (-inf,0] and [0,inf).

ArctanAsymptote is approximately linear in [-0.5,0.5], and is useful out to the range [-1e15,1e15], though with much reduced precision for larger values.