Consider calling besselj(n, x) where x is negative, while n is a large negative integer:
julia> Bessels.besselj(-172, -2.0)
NaN
julia> Bessels.besselj(-37, -2.0f0)
NaN32
When at least one argument is positive, there is no problem:
julia> Bessels.besselj(172, -2.0)
4.657823561745e-312
julia> Bessels.besselj(-37, 2.0f0)
-7.1f-44