Added supported for gamma function.

[newptcai]

Changes

• added a Project.toml
• updated the code to work with latest packages
• added code to call ArbNumercs.jl

Note that there is some problem with erfinv and erfcinv. Some old test cases can not finish in reasonable time. I have commented them out.

[dpsanders]

Sorry for the delay in seeing this and thanks for the contribution!

Do you have any idea what the problem is?

[dpsanders]

It looks like the failures are on Julia 0.6 (!) which we no longer should support.

Would you mind adding a Project.toml and testing on Julia 1.4?

[newptcai]

Sorry I am getting a bit busy. Maybe this can wait a while?

[dpsanders]

Yes of course, no rush - thanks!

[newptcai]

The problem with erfinv is that in

function _erfinv(a::T) where T
    domain = Interval{T}(-1, 1)
    a ∉ domain && return DomainError("$a is not in [-1, 1]")
    f = x -> erf(x) - a
    fp = x->2/sqrt(pi_interval(T)) * exp(-x^2)
    rts = roots(f, fp, Interval{T}(-Inf, Inf), Krawczyk, 1e-20)
    @assert length(rts) == 1 # && rts[1].status == :unique

    rts[1].interval
end

The call to roots get stuck and never returns. That's why I commented out tests for erfinv and erfinvc.

[dpsanders]

What's the status here?

[dpsanders]

Cross-reference to the original issue in IntervalArithmetic.jl:

JuliaIntervals/IntervalArithmetic.jl#372

[AnderGray]

@newptcai @dpsanders Any updates? Would be a useful thing to have :)