arcsinvnv

Arcsinvnv is a term that appears in mathematical notation and programming libraries but does not have a single, universally accepted definition. In practice, it is often used to denote a variant of the inverse sine operation that includes input normalization or scaling by a parameter denoted nv, with the aim of improving numerical stability or mapping values into a standard domain.

A common interpretation in software contexts is arcsinvnv(x, nv) = arcsin(clamp(x / nv, -1, 1)), where nv is a nonzero real parameter that scales the input and clamp restricts the argument to the interval [-1, 1]. In this form, arcsinvnv returns an angle in the range [-pi/2, pi/2]. If the implementation omits the clamp, it typically assumes that |x| <= |nv| for valid input.

Variants exist. Some definitions omit clamp and require the user to guarantee that |x| <= nv, while others treat nv as a function or dynamic range parameter. The derivative, when the un-clamped form is used and |x| < nv, is d/dx arcsin(x/nv) = 1 / (nv * sqrt(1 - (x/nv)^2)).

Examples illustrate usage: arcsinvnv(0.5, 2) equals arcsin(0.25). Different libraries may document this function differently, and in some contexts arcsinvnv may refer to a shorthand for a normalized inverse sine operation rather than a distinct mathematical function.

Because arcsinvnv is not standardized, users should consult the specific documentation of the library or paper in which it appears to confirm its exact definition, domain, and applications.