⚠️ arithmetic operations with Inf

[mtanneau]

If we want to be able to use Multifloats.jl, we need to be careful about arithmetic operations with Inf.
Our current implementation relies on conventions like Inf + 1 == Inf and -1 * Inf == -Inf, from which Multifloats.jl deviates.
After taking a quick glance, it shouldn't be too hard for us to add manual checks to avoid arithmetic operations with Inf when possible.

Pointers: here and here.

We can also add Float64x2 to the tests.

[joehuchette]

+1 to exploring higher precision floats, and that compliance with IEEE standard handling of Infs and NaNs is probably not going to be all that important.

Relatedly, @Anhtu07 had a question about handling Inf in presolve routines, since 1e30 is used as a sentinel value for infinity in a number of solvers (and the presolve "bible" paper).

[mtanneau]

Historically, the handling of Inf was not clear in C and not always supported (Infinity was introduced in C99, possibly after some solvers were written). Fortunately, we don't have to deal with that :)

1e30 is used as a sentinel value for infinity in a number of solvers

My preference would be that all the routines handle finite and infinite values equally well; provided the arithmetic follows some conventions on the handling of Inf.

If we choose to have a cutoff value M and round larger values to ±Inf, then I would see it as a user-modifiable parameter, with arithmetic-aware default values.
Likewise, we could have some drop tolerance and round small coefficients/bounds to zero.

I would see that cleaning be performed once at the beginning of presolve, and (at least as a user), I would want to see a warning if some values were dropped/rounded to infinity.