Fun with floats

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1

I am on a x86_64 machine, in the ocaml-5.1.0 toplevel:

# 1.0 = 1.0 -. min_float;;
- : bool = true

I was surprised by this one.
So, I looked for the smallest float I can get that have the desired behavior:

1.0 = 1.0 -. 0.0000000000000001;;
- : bool = false

So now, I can draw a float in [0, 1[ (“0.0 included, 1.0 excluded”) like this:

let epsilon =  0.0000000000000001;;
let almost_one = 1.0 -. epsilon;;
let rand = Random.float almost_one;;

I also thought about an (recursive but still) ugly solution:
call Random.float 1.0 until you get something <1.0.

2

You didn’t ask about it, but in case other readers are wondering about it, this is because the precision of floating-point numbers depends on the exponent of the number being represented (this is what makes it “floating” instead of “fixed”), and for 1.0, the maximum precision is smaller than min_float, so that adding or substracting min_float does not have any effect. More generally, this phenomenon is quantified by the “unit in the last place” (ULP): Unit in the last place - Wikipedia.

You can also use Float.pred 1.0.

Cheers,
NIcolas

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3

I did not know about the existence of Float.pred, thanks!

4

Note that this solution (rejection sampling) is just fine, given that you will never get 1.0 in practice if you call Random.float 1.0. (With the current implementation I believe that the probability for this to happen is 2^{-53}, modulo floating-point approximations).

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