KSampleADTest fails on 32-bit with longer data arrays

[oschulz]

On 32-bit systems (tested on 32-bit Linux), KSampleADTest starts to fail when the data arrays grow larger (not really all that large):

julia> using HypothesisTests

julia> pvalue(KSampleADTest(randn(100), randn(100)))
0.4684450603589013

julia> pvalue(KSampleADTest(randn(1000), randn(1000)))
ERROR: DomainError with -0.008755839260454446:
sqrt will only return a complex result if called with a complex argument. Try sqrt(Complex(x)).
[...]

julia> pvalue(KSampleADTest(randn(50000), randn(50000)))
NaN

julia> versioninfo()
Julia Version 1.6.2
Commit 1b93d53fc4 (2021-07-14 15:36 UTC)
Platform Info:
  OS: Linux (i686-pc-linux-gnu)
  CPU: Intel(R) Core(TM) i9-9880H CPU @ 2.30GHz
  WORD_SIZE: 32
  LIBM: libopenlibm
  LLVM: libLLVM-11.0.1 (ORCJIT, skylake)

On 64-bit, the above runs fine.

[oschulz]

Same happens with ApproximateTwoSampleKSTest. I think for the KS-test it's due to this:

function pvalue(x::ApproximateTwoSampleKSTest; tail=:both)
    n = x.n_x*x.n_y/(x.n_x+x.n_y)
    #...
end

We could use float(x.n_x) * float(x.n_y) or so to prevent the integer overflow in the product.

[nalimilan]

Or maybe just doing n = x.n_x*(x.n_y/(x.n_x+x.n_y))? Anyway feel free to make a PR.

[oschulz]

I'll put it on my to-do list. :-)