Repeat a function N times in Julia (composition)

Question

I'm trying to make a function that compose a function f(x) by itself N times, something like that:

function CompositionN(f,N)
             for i in 1:N
                f(x) = f(f(x))
             end
return f(x)

I need that the function CompositionN returns another function, not a value.

Answer 1

The solution with ntuple and splatting works very well up to a certain number of compositions, say 10, and then falls off a performance cliff.

An alternative solution, using reduce, is fast for large numbers of compositions, n, but comparatively slow for small numbers:

compose_(f, n) = reduce(∘, ntuple(_ -> f, n))

I think that the following solution is optimal for both large and small n:

function compose(f, n)
    function (x)  # <- this is syntax for an anonymous function
        val = f(x)
        for _ in 2:n
            val = f(val)
        end
        return val
    end
end

BTW: it is the construction of the composed function which is faster in the approach suggested here. The runtimes of the resulting functions seem to be identical.