Reduce the range of elements sorted by partialsort

[LilithHafner]

missing means the end of the vector (e.g. PartialQuickSort(missing, missing) === QuickSort). There is no need to sort the elements begin:k-1 for partialsort(k).

Fixup for #45222

julia> @btime partialsort(rand(10_000), 10_000)
@btime sort(rand(10_000), alg=PartialQuickSort(10_000))
  526.527 μs (8 allocations: 312.69 KiB)
0.9998857291289974

julia> @btime sort(rand(10_000), alg=PartialQuickSort(10_000))
@btime sort(rand(10_000), alg=PartialQuickSort(missing, 10_000))[10_000]
  517.977 μs (8 allocations: 312.69 KiB)
 0.9999893337886981

julia> @btime sort(rand(10_000), alg=PartialQuickSort(missing, 10_000))[10_000]
  521.084 μs (8 allocations: 312.69 KiB)
 0.999986247898864

julia> @btime sort(rand(10_000), alg=PartialQuickSort(10_000, 10_000))[10_000]
  67.384 μs (8 allocations: 312.69 KiB)
 0.9997135092971121

[petvana]

I may miss something, but this PR seems to be in a conflict with the original documentation, and thus breaking

PartialQuickSort{T <: Union{Integer,OrdinalRange}}

  Indicate that a sorting function should use the partial quick sort algorithm. Partial quick sort
  returns the smallest k elements sorted from smallest to largest, finding them and sorting them using
  QuickSort.

[LilithHafner]

That's probably why I overlooked it in the last PR.

However, partialsort(v, ::Integer) and friends only return a single element and are not documented to sort the beginning of the vector, so we may still use PartialQuickSort(k, k) internally.

julia> partialsort(rand(1000), 500)
0.5000542824047202

I'll make the corresponding changes.

[petvana]

Thanks. Shouldn't we also include the removed documentation for PartialQuickSort(k::Integer)?

[LilithHafner]

I'm not a huge fan of PartialQuickSort(k) meaning "sort the first k elements" while partialsort!(v, k) means "put the kth element in place", so I'm inclined to leave the docstring out and replace it with a comment noting that PartialQuickSort(k) = PartialQuickSort(missing, k) is needed for compatability reasons.

Is the undocumentation of a feature (provided it is still supported) something we can do before 2.0?

[petvana]

Ok. Can we at least deprecate it if we remove the docs? Smth like this?

@deprecate PartialQuickSort(k::Integer) PartialQuickSort(1:k)

Results in this

$ julia --depwarn=yes             |

julia> import Base: PartialQuickSort

julia> @deprecate PartialQuickSort(k::Integer) PartialQuickSort(1:k)
PartialQuickSort

julia> PartialQuickSort(5)
┌ Warning: `PartialQuickSort(k::Integer)` is deprecated, use `PartialQuickSort(1:k)` instead.
│   caller = ip:0x0
└ @ Core :-1
PartialQuickSort{UnitRange{Int64}}(1:5)

[LilithHafner]

I decided to do that separately because I think both PRs stand on their own and they have substantially different motivations.

[LilithHafner]

It took a few turns to get here, but I believe this PR is currently a simple performance improvement and the CI failures are unrelated.

sortperm(v, k::Integer) will no longer sort the beginning of v, but it was never documented to do so.

[petvana]

If CI failures are really unrelated then the PR seems ready to be merged.

[LilithHafner]

Typically folks express that sentiment with an approving PR review, but a comment works too :)