Support for BigFloat arguments

[fda-tome]

Why cant we get arbitrary precision on the besselj functions?

[heltonmc]

Thanks for the interest! This is definitely on the radar but not implemented. You’re best bet for arbitrary precision is to use ArbNumerics.jl which wraps the fantastic Arb library. There you can specify any precision you want to compute rigorously ‘besselj’.

The reason they are not currently implemented is that the implementations for arbitrary precision routines and fixed precision to double precision are different. I have no plans to support arbitrary precision with this library as I think Arb is excellent. However, I do have some plans to support Float128 or Double64 in the future. I can’t say I’ll ever get there for sure but I have wanted that functionality.

For now, ArbNumerics.jl or QuadMath.jl will be your best bet ☺️

[fda-tome]

Awesome! I am very interested in implementing Float128 and Double64 support, I got a lot on my plate right now with GSOC, but once I'm finished with it Ill be happy to tag in and contribute. 😄

[heltonmc]

Sounds good! Happy to help with that so please feel free to ask any questions when you have more time!

[nsajko]

Regarding the original topic of this issue (BigFloat support), note that MPFR already implements the relevant functionality and the SpecialFunctions package already wraps the MPFR interface. E.g.:

julia> using SpecialFunctions

julia> let x = one(BigFloat) / 3
         besselj0(x) == besselj(0, x)
       end
true

Not to discourage a pure-Julia implementation, though.

Regarding support for fixed-precision FP types like Float128, maybe I give implementing those a try myself, after improving some parts of the Float32 and Float64 implementations.