Base.rand() produces too many collisions for `Float32`s

[simsurace]

Minimal working example (Tested on Julia 1.5 and 1.6.)

julia> A = rand(Float32, 2^20);
julia> length(A)-length(unique(A))

Expected behavior
The expected number of duplicates when drawing n times at random from a set of N elements with replacement is equal to (see e.g. Proposition 4.1 in this paper)

expected_number_of_duplicates(N, n) = n - N * (1 - (1 - 1/N)^n)

For drawing a uniform Float32, we therefore expect

julia> expected_number_of_duplicates(2^32, 2^20)
127.98946189880371

Actual behavior
I obtain numbers that are on the order of 60000.

[sostock]

But the set doesn’t have 2^32 elements, since only numbers in the interval [0,1) are returned by rand.

[oscardssmith]

Also, rand doesn't generate all numbers in [0,1). It generates only numbers from [1,2).-1. As such, there are 2^23 different possible return values. As such,

expected_number_of_duplicates(2^23, 2^20)
62888.521840296686

which seems in line with the number you're seeing. Given that, should this be closed?

[simsurace]

Oh yes, of course! Apologies and thanks for clearing this up.