Closed01: distribution that generates floats in the range [0, 1]

[abonander]

Background

What is your motivation?

My current work project involves a networking and utility library that is primarily targeted at Unity developers, with a core written in Rust.

Without going into details currently under NDA, we're trying to provide a higher quality/more featureful substitute for Unity's Random class, which has the idiosyncrasy that it generates floats in the closed range [0, 1]: https://docs.unity3d.com/ScriptReference/Random-value.html

Of course, it's relatively simple to implement this with Uniform::new_inclusive(0f64, 1f64), but its constructor does non-trivial work which means we either need to keep an instance cached somewhere (which is what we're currently doing) or pay the cost every time we want to generate a float.

What type of application is this? (E.g. cryptography, game, numerical simulation)

Games.

Feature request

Provide a new distribution, Closed01, similar to Open01 and OpenClosed01, that generates f32s and f64s in the range [0, 1].

This would complete the set of distributions covering this range:

• Standard: sampling in [0, 1)
• Open01: sampling in (0, 1)
• OpenClosed01: sampling in (0, 1]
• (proposed) Closed01, sampling in [0, 1]

[josephlr]

One thing to consider here is that a "fully accurate" implementation of sampling on [0,1] essentially will never select 0, so in practice OpenClosed01 should be OK. See #1346 for a longer discussion.

For example, if we select a real number x uniformly at random from the interval [0,1], the probability x <= f64::MIN_POSITIVE is 2^(-1022), so it should literally never happen.

In my opinion, there should probably only be two distributions for selecting floats between 0 and 1, based on the following two (idealized) processes:

1. Select a real number uniformly at random from [0,1], then round to the nearest floating point number. This is what's described in Higher quality (0, 1] floats #1346 and would sometimes select 1 and ~never select 0, so it would work like OpenClosed01.
2. Select a real number uniformly at random from [0,1], then round down to a floating point number. This would never select 1 and ~never select 0, so it would work like Open01.

Standard would then be an alias for one of these distributions.

[abonander]

Hmm, the documentation for Unity's Random.value states:

Any given float value between 0.0 and 1.0, including both 0.0 and 1.0, will appear on average approximately once every ten million random samples.

It sounds like they're making a significant sacrifice in precision in order to guarantee full coverage of the range.

That may make sense for an implementation specialized for games but I can appreciate why it wouldn't necessarily be useful for a general-purpose library.

[josephlr]

Hmm, the documentation for Unity's Random.value states:

Any given float value between 0.0 and 1.0, including both 0.0 and 1.0, will appear on average approximately once every ten million random samples.

It sounds like they're making a significant sacrifice in precision in order to guarantee full coverage of the range.

Unity's documentation is definitely wrong here, as:

1. The floats between 0 and 1 are not evenly spaced
2. There are more than 10 million f32 values between 0 and 1

EDIT: My guess is that they are generating a random float in the range [1,2] (of which there are 2^23 + 1 = 8.4 Million of) and then subtracting 1. This does not hit every value in [0,1], but isn't the worst algorithm in the world. We do something similar in the Uniform implementation.

[abonander]

Okay, I'm actually starting to grok the problem now.

For one, I for some reason thought that Random.value returned a double (f64) which is why I thought it was sacrificing precision, but float/f32 makes more sense for game engines.

Anyway, I think any non-expert would see "uniformly distributed between 0 and 1 (inclusive)" and interpret that as "just as likely to be in the range [0.9, 1.0] as [0, 0.1] (or anywhere in between)".

The fact that the actual set of numbers is not evenly spaced is an idiosyncrasy of floating-point representation that I think most people won't really care or want to think about.

IMO, a specialized version of Uniform::new_inclusive(0.0, 1.0) with 23/52 bits of precision is perfectly fine for most intents and purposes. If someone needs more precision than that, well, they probably shouldn't be using floating-point in the first place.

FWIW, we ended up deciding not to implement this exact behavior at the Rust level anyway.

[dhardy]

Closing.

FYI, just using Standard or OpenClosed01 should satisfy nearly every use-case, especially with f64 where the chance of sampling exactly zero or one is extremely low.