I wanted to ask about the output distribution of floating-point rand(): Naively, I would have expected the following distribution: -the sign bit is zero -the mantissa is a random bitstring -the signigicant is an exponentially distributed integer, e.g. const-leading_zeros of an infinite bitstream …

So it took me a bit to grok what all is going on here. This getfloat_trail function transforms a random UInt32 to a Float32. This is different from our current rand(::Float32) — which is approximated here by getfloat_std — in the following ways: Its output is in (0,1) instead of [0,1). 32 bits i…

Is this distribution standard / intended? This is how dSFMT, which is used internally works: it only generates 52 random bits at a time, and uses that to produce a random Float64 in [1, 2), to which 1 is substracted. Nowadays, we do the substraction on the Julia side. So yes this is intended, and…

Thanks. A “correct” [0,1)-float would take 54 bits of entropy, instead of 52; alas, with a variable bit-rate encoding. Reason for asking was that I was thinking about submitting a PR for a CSPRNG, and as far as I understood, there is currently no generic structure that does buffering and conversion…

Ok, I did some benchmarking. The distribution is mainly a problem for Float32. I think the following variant is competitive, and gives a much smoother distribution near 0, because we use the entire 32 bits of entropy: julia> using Random julia> using BenchmarkTools julia> N=20_000; inp=rand(UInt32,…

Because this came up on hackernews and the timings are really old, current (julia 1.9.2): julia> @btime Random.rand!($inp); 2.493 μs (0 allocations: 0 bytes) julia> @btime Random.rand!($outp); 3.012 μs (0 allocations: 0 bytes) julia> @btime broadcast!($getfloat_std, $outp, $inp); 1.339 μs (…

I opened a new thread on Output distribution of rand(), thread 2 to discuss the issue, separated from my old solution attempt. I think throwing some half-baked @benchmark around was premature and an impediment to a serious discussion. My bad, I should have opened with a better thread 5 years ago. B…

Output distribution of rand()

Internals & Design

mbauman Closed October 19, 2023, 1:22pm 9

Closing to focus discussion in Output distribution of rand(), thread 2

Topic		Replies	Views
Output distribution of rand(Float32) and rand(Float64), thread 2 Internals & Design float , random	437	10127	November 19, 2023
Are rand(Float32) really uniform in [0,1)? General Usage question	29	1323	November 5, 2025
Frédéric Goualard found an inexactness in our rand() Numerics random	19	1186	September 8, 2022
Is it really possible for rand to throw a zero? Statistics question	61	4915	September 18, 2019
Random number in (0,1] General Usage	16	15188	October 8, 2018

Output distribution of rand()

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