Call user function only once in `mean`

[nalimilan]

Override the standard mapreduce machinery to promote accumulator type. This avoid calling the function twice, which can be confusing.

Fixes #49 but with a more general solution than https://github.com/JuliaStats/Statistics.jl/pull/80/.

Cc: @stevengj @kagalenko-m-b

Unfortunately, performance drops for a Float64 vector:

julia> x = rand(100_000_000);

julia> y = ifelse.(rand(Bool, length(x)) .> .25, missing, x);

julia> z = Vector{Union{Missing, Float64, Int}}(y);

julia> z .= ifelse.(rand(Bool, length(y)) .> .25, round.(Int, x), z);

# master
julia> @btime mean(x);
  68.582 ms (1 allocation: 16 bytes)

julia> @btime mean(y);
  472.870 ms (1 allocation: 16 bytes)

julia> @btime mean(z);
  533.646 ms (3 allocations: 48 bytes)

# PR
julia> @btime mean(x);
  128.785 ms (4 allocations: 64 bytes)

julia> @btime mean(y);
  506.305 ms (1 allocation: 16 bytes)

julia> @btime mean(z);
  598.425 ms (1 allocation: 16 bytes)

This is simply due to sum being slower when init is provided as it calls mapfoldl under the hood in that case:

julia> @btime sum(x);
  68.199 ms (1 allocation: 16 bytes)

julia> @btime sum(x, init=0.0);
  124.127 ms (1 allocation: 16 bytes)

[nalimilan]

The new commit implements a simpler approach which is fast for concrete eltypes but super slow for complex type unions as the compiler doesn't infer an element type more precise than Any

julia> @btime mean(x);
  68.529 ms (4 allocations: 64 bytes)

julia> @btime mean(y);
  550.489 ms (0 allocations: 0 bytes)

julia> @btime mean(z);
  2.752 s (25300984 allocations: 386.06 MiB)

[kagalenko-m-b]

It looks like you're reimplementing undocumented Base internals, doesn't that have potential to break in future Julia versions?

[nalimilan]

Yes, but given that Statistics is an stdlib any breakage would be noticed in Julia even before merging it. I'm more concerned about performance issues introduced by the PR...