add more methods and tests for reductions over empty arrays

[simonbyrne]

From discussion in #28535.

[vtjnash]

Can you update this so that the doctest passes?

[StefanKarpinski]

Bump. Needs doctest fixes. Otherwise good to go.

[timholy]

Now that we have maximum(itr; init=typemin(eltype(itr))), is this really the way we want to go? What if someone wanted the error? The init approach lets the user/developer choose.

#41885 will print a nice warning suggesting to supply an init value.

[timholy]

But 👍 to more tests!

[tkf]

Is it OK to get false from -1 <= maximum(sin.(xs)) <= 1? (I prefer an error)

[oscardssmith]

Let's figure out if this is OK to merge and then merge it.

[tkf]

FWIW, I'm opposed to this change. We don't know the domain on which the user data is defined and we don't know if typemin and typemax are meaningful values (see an example above). I think nudging users to specify the identity element via init will help them write more robust programs.

That said, I think the following tweaks might make sense if we go with this.

[JeffBezanson]

Triage thinks it's ok to add these, with tkf's suggestions. maximum(sin.(xs)) where xs is empty is unfortunate, but all you're doing is passing an empty array to maximum, so it doesn't matter how you got it. maximum(sin, xs) is different, and should remain an error.