Are rand(Float32) really uniform in [0,1)?

[mbauman]

@FattiMei

What is the metric to compare all the generation schemes proposed so far?

First you need to define what a uniform distribution means in the first place. The best formal meaning I have for our current definition is:

rand(Float32) < p has probability p of being true for all p that are multiples of 2^{-24} in [0, 1]. Note that the Float32s in [0.5, 1] are the multiples of 2^{-24}. The exact inequality operator here matters, as does the precision of p. It matters how you use it!

Output distribution of rand(Float32) and rand(Float64), thread 2

This is a fun problem. Here’s my crack at it: function randf( ::Type{T}, u::UInt64 = rand(UInt64), ) where {T<:Union{Float16,Float32,Float64}} # only depends on T s = 8*sizeof(T) p = Base._precision(T) - 1 U = T === Float16 ? UInt16 : T === Float32 ? UInt32 : T === Float64 ? UInt64 : error() m = T === Float16 ? one(T) : inv(reinterpret(T, U(65 << p))) # real computation z = leading_zeros(u) if T !== Float16 b = (u << (z + …

Output distribution of rand(Float32) and rand(Float64), thread 2

So on the [0,1) vs (0,1] thing, it has everything to do with how you interpret and work with the results of rand() — and I finally have a good mental model here. Forget binary for a moment; let’s pretend our datatype of interest is decimal-based float with two digits and has a random function defined as randpct() = rand(0:99)/100. Given that definition, how do I implement a test that returns true 5% of the time? I know I just instinctively reach for randpct() < 0.05. But why <? And why not <=…