Unify rounding code

[fingolfin]

Systematically provide methods for ceil, floor, round, trunc with various source and/or target types we provide. Remove some (accidental?) type piracy.

For m a Matrix{BigFloat} instead of trunc(m) one now needs to write trunc(ZZMatrix, m) which avoids type piracy. On the upside, this is now supported for any Matrix{<:Real}.

Also add methods is_positive(::QQFieldElem) and is_negative(::QQFieldElem), move some functions to more appropriate places, and "optimize" (?) sign(::Type{Int}, a::QQFieldElem).

See also #1495

[codecov]

Codecov Report

Merging #1540 (b4ec113) into master (a02b817) will increase coverage by 0.16%.
The diff coverage is 82.14%.

@@            Coverage Diff             @@
##           master    #1540      +/-   ##
==========================================
+ Coverage   84.03%   84.19%   +0.16%     
==========================================
  Files          94       94              
  Lines       36614    36614              
==========================================
+ Hits        30767    30826      +59     
+ Misses       5847     5788      -59     

Files	Coverage Δ
src/HeckeMiscInteger.jl	22.59% <100.00%> (+7.98%)	⬆️
src/HeckeMoreStuff.jl	2.84% <ø> (+0.32%)	⬆️
src/flint/fmpz.jl	91.45% <66.66%> (+0.04%)	⬆️
src/flint/fmpq.jl	85.03% <79.48%> (-0.72%)	⬇️

... and 4 files with indirect coverage changes

📣 We’re building smart automated test selection to slash your CI/CD build times. Learn more

[fingolfin]

This PR got a bit out of hand 😅 but it should be there now.

[thofma]

It seems that code coverage for the changes is below 50%? Is this a fluke?

[fingolfin]

Part of this PR is moving a lot of untested code around. While I added some tests for new stuff I added, I did not e.g. add tests for the various round methods for QQFieldElem, so all of this drags the coverage down.

But I've now taken the time to add some (and of course once again found and fixed issues in the existing untested code 🙄 ).

[fingolfin]

BTW this is now handled by generic code (in the macro) which also supports e.g. Float64 and more

[thofma]

The Oscar error looks real: https://github.com/Nemocas/Nemo.jl/actions/runs/6411567510/job/17444653341?pr=1540

Any idea what is going on?

[benlorenz]

The Oscar error looks real: Nemocas/Nemo.jl/actions/runs/6411567510/job/17444653341?pr=1540

Any idea what is going on?

https://github.com/thofma/Hecke.jl/blob/b3fdace2a0a75dc21d7bd1480298ebdfbae6237b/src/QuadForm/indefiniteLLL.jl#L300-L301:

  U3 = identity_matrix(ZZ,n)
  U3[n,1] = round(- G3[n,n]//2*1//G3[1,n])

The return value of the round seems to be a QQFieldElem now which doesn't want to be assigned to the ZZMatrix?

Old:

function Base.round(a::QQFieldElem)
    return round(ZZRingElem, a)
end

vs new:

Base.round(a::QQFieldElem) = round(QQFieldElem, a)

[lgoettgens]

To mimic the behavior of Base for Float, I would say that the new behavior is better (cf https://docs.julialang.org/en/v1/base/math/#Base.round-Tuple{Type,%20Any}).

[fingolfin]

The documentation of round states:

round([T,] x, [r::RoundingMode])
round(x, [r::RoundingMode]; digits::Integer=0, base = 10)
round(x, [r::RoundingMode]; sigdigits::Integer, base = 10)

Rounds the number x.

Without keyword arguments, x is rounded to an integer value, returning a value of type
T, or of the same type of x if no T is provided.

That round(::QQFieldElem) returned a ZZRingElem violated that, and so I "fixed it".

But of course I can reverse that -- or mark this PR as "breaking" and we just update callsites, I don't think there'll be many, and the fix is trivial (just add ZZRingElem as first argument).

[thofma]

Let's mark this breaking and fix the callsites when bumping the dependency.

[fingolfin]

OK. I am going to release AA now, then Nemo, then... we'll see ;-)

[Krastanov]

I am seeing a ton of new errors reported by Aqua in my CI when it runs with the new version of Nemo.

https://github.com/QuantumSavory/QuantumClifford.jl/actions/runs/6451102837/job/17511289576?pr=193

If I understand correctly, it due to the changes made here.