Fix division of two negative FastRational{BigInt}

[Liozou]

Currently:

julia> FastQBig(-1) / FastQBig(-1)
ERROR: MethodError: no method matching typemax(::Type{BigInt})
Closest candidates are:
  typemax(::Type{LibGit2.Consts.GIT_MERGE_FILE_FAVOR}) at Enums.jl:191
  typemax(::Type{MbedTLS.CipherMode}) at Enums.jl:191
  typemax(::Type{Pkg.GitTools.GitMode}) at Enums.jl:191
  ...
Stacktrace:
 [1] /(::FastRational{BigInt}, ::FastRational{BigInt}) at /home/liozou/.julia/dev/FastRationals/src/generic.jl:120
 [2] top-level scope at none:1

as with any division of two negative FastRational{BigInt}, which hit me today as soon as I tried going from Rational{BigInt} to FastRational{BigInt}.

This PR fixes this by adding a specialized method for /(x::FastRational{T}, y::FastRational{T}) where {T<:BigInt} that simply bypasses the check with typemax(T). It's not a very clever fix, but I could not find another way to implement it that did not have any performance hit. In particular, I tried adding an isapplicable(typemax, T) check but T was not const-propagated (which is not a surprise I think), or, alternatively, hasmethod(typemax, Tuple{Type{BigInt}}) but it does not specialize on its arguments. If anyone has any idea, I will gladly update the PR! But in the meantime it does the job.

I added FastQBig among the tests (as well as the particular bug this PR fixes). Some tests that were commented out and marked with a # FIXME!!! actually work so I uncommented them. Let me know if this is a mistake!

[JeffreySarnoff]

good -- thank you

[JeffreySarnoff]

Please let me know how you use the package, what you do with it.

[JeffreySarnoff]

Your contribution is part of the current version of FastRationals.
After unpinning your development version and, optionally, removing FastRationals:
julia> using Pkg; Pkg.update() or, optionally,
julia> using Pkg; Pkg.add("FastRationals") should pull it in for you.

[Liozou]

Wow, that was really fast, thanks!
I am working with periodic graphs and I need to compute a set of positions such that each vertex is at the average position of that of its neighbours. Since I actually want the mathematically exact solution, this amounts to solving a linear system with rational BigInts. Using FastRationals does give me some performance improvement on small systems, but it's slower on big systems (around 600 vertices per unit cell) most probably because the BigInts get prohibitively large during my LU decomposition. So I might not use the package eventually, or maybe only as an optimization once I figure for which case it does provide some speedup. But for the moment I have other issues to tackle first so I'll see about that later.

Anyway, glad I could help with that and thanks for the very fast merge!

[Liozou]

I just now discovered the function Base.hastypemax which was exactly what I was looking for... So I guess the change can be rewritten nicely. But it working is probably more important anyway.

[JeffreySarnoff]

go ahead and PR that rewrite, please