Support specific mapreduce

[putianyi889]

Since sum, maximum, etc. lower to mapreduce, it might be a better idea to support mapreduce(f, op, ::AbstractFill) for op at least in (:max, :min :+, :|, :&) to support maximum, minimum, sum, any and all.

Examples:

Base.mapreduce(f, ::typeof(max), A::Fill) = f(A.value)
Base.mapreduce(f, ::typeof(+), A::Fill) = length(A)*f(A.value)

[jishnub]

Currently, these should be handled by

FillArrays.jl/src/fillbroadcast.jl

Lines 35 to 52 in 7036a50

	function Base._mapreduce_dim(f, op, ::Base._InitialValue, A::AbstractFill, ::Colon)
	fval = f(getindex_value(A))
	out = fval
	for _ in 2:length(A)
	out = op(out, fval)
	end
	out
	end
	function Base._mapreduce_dim(f, op, ::Base._InitialValue, A::AbstractFill, dims)
	fval = f(getindex_value(A))
	red = *(ntuple(d -> d in dims ? size(A,d) : 1, ndims(A))...)
	out = fval
	for _ in 2:red
	out = op(out, fval)
	end
	Fill(out, ntuple(d -> d in dims ? Base.OneTo(1) : axes(A,d), ndims(A)))
	end

but it might be better to specialize mapreduce instead of this internal function.

The loop seems elided already:

julia> f = Fill(3, 100_000);

julia> @btime maximum($f);
  2.944 ns (0 allocations: 0 bytes)

[putianyi889]

maximum is achieved by https://github.com/JuliaArrays/FillArrays.jl/blob/master/src/FillArrays.jl#L558-L560

for op in (:maximum, :minimum)
    @eval $op(x::AbstractFill) = getindex_value(x)
end

Anyway, mapreduce currently is not specialized:

julia> C = Fill(1,10000000)
10000000-element Fill{Int64}, with entries equal to 1

julia> @time mapreduce(identity, max, C)
  0.000705 seconds (2 allocations: 64 bytes)
1

julia> C = Fill(1,100000000)
100000000-element Fill{Int64}, with entries equal to 1

julia> @time mapreduce(identity, max, C)
  0.006655 seconds (2 allocations: 64 bytes)
1