# Random number in (0,1\]
**URL:** https://discourse.julialang.org/t/random-number-in-0-1/16009
**Category:** General Usage
**Created:** [October 8, 2018, 6:14am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009 "2018-10-08T06:14:34Z")
**Posts on this page:** 17
**Page:** 1
### Author:  [@greg\_plowman](https://discourse.julialang.org/u/greg_plowman)
#### Post date: [October 8, 2018, 6:14am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/1 "2018-10-08T06:14:34Z")
I want a random `Float64` in the interval `(0,1]`.
I understand `rand()` returns a number in `[0,1)`.
Should I just use `1-rand()` ?
---
### Author:  [@xiaodai](https://discourse.julialang.org/u/xiaodai)
#### Post date: [October 8, 2018, 6:31am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/2 "2018-10-08T06:31:52Z")
is `rand()` not more like `(0,1)`? And how much does `[0,1)` matter vs `(0,1]`? For most numerical problems, I assume the distinct makes no different what-so-ever in practice.
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [October 8, 2018, 7:16am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/3 "2018-10-08T07:16:03Z")
> [@greg\_plowman](#):
>
> Should I just use `1-rand()` ?
That’s a nice and quick solution. You can also check for `1` and make it into a `0`, eg
```julia
rand(Float64) |> x -> iszero(x) ? one(x) : x
```
---
### Author:  [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)
#### Post date: [October 8, 2018, 7:37am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/4 "2018-10-08T07:37:22Z")
You should not use `1.0 - rand()`.
The density of Float64s (how many occur within a subspan) varies within [0.0,1.0].
(source: [Float](https://ridiculousfish.com/blog/posts/float.html))
(source: [Luis R. Izquierdo and J. Gary Polhill: Is Your Model Susceptible to Floating-Point Errors?](http://jasss.soc.surrey.ac.uk/9/4/4.html))
for a single random Float64 in (0.0, 1.0]
```julia
randfloat = rand()
if randfloat === 0.0
randfloat = 1.0
end
```
for n of them
```julia
zerosasones(x) = ifelse(x === 0.0, 1.0, x)
randfloats = zerosasones.(rand(n))
```
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [October 8, 2018, 7:56am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/5 "2018-10-08T07:56:21Z")
> [@JeffreySarnoff](#):
>
> The density of Float64s (how many occur within a subspan) varies within [0.0,1.0].
I am not sure how that is relevant, AFAIK `rand` accounts for that and the result is uniform.
---
### Author:  [@bkamins](https://discourse.julialang.org/u/bkamins)
#### Post date: [October 8, 2018, 8:06am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/6 "2018-10-08T08:06:02Z")
The density is varying but `rand()` does sample from it uniformly as it actually samples from `[1,2[` and subtracts `1.0`.
This is equivalent to running `2.0-rand(Random.CloseOpen12())` which avoids this subtraction.
You can check it by running:
```julia
julia> function t(m1, m2)
x = 1.0 - rand(m1)
y = 2.0 - rand(m2, Random.CloseOpen12())
x == y
end
t (generic function with 2 methods)
julia> m1, m2 = MersenneTwister(100), MersenneTwister(100);
julia> all(t(m1,m2) for i in 1:10^8)
true
```
The key thing here is that on `[1,2[` interval all `Float64` are uniform. You can check that `eps` for any value in `[1,2[` range is the same. as well as the difference between `x` and `nextfloat(x)` in this range.
In other words if you look at [Luis R. Izquierdo and J. Gary Polhill: Is Your Model Susceptible to Floating-Point Errors?](http://jasss.soc.surrey.ac.uk/9/4/4.html) image `[1,2[` just happens to be one subsegments that is uniform on it.
Actually on [Float](https://ridiculousfish.com/blog/posts/float.html) it is shown on this picture:
---
### Author:  [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)
#### Post date: [October 8, 2018, 8:13am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/7 "2018-10-08T08:13:23Z")
```julia
using StatsBase: skewness
rs01 = rand(n)
rs10 = 1.0 .- rs01
skewness(rs01) == -skewness(rs10)
```
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [October 8, 2018, 8:15am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/8 "2018-10-08T08:15:16Z")
You are demonstrating numerical error (after correcting to `rs10 = 1.0 .- rs01`, which makes it run).
---
### Author:  [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)
#### Post date: [October 8, 2018, 8:18am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/9 "2018-10-08T08:18:12Z")
I am demonstrating skewness in small random samples and that it swaps signs using `1.0 .- rand()`
More to the point, a uniform random number generator returning values in [0.0, 1.0) is used internally in simulation code that requires random variates from some specific non-unform distribution, often also in [0.0, 1.0). Once that happens, using one minus random variate probably maps some distinct smaller numbers together as they cross power of 2 bounds.
---
### Author:  [@bkamins](https://discourse.julialang.org/u/bkamins)
#### Post date: [October 8, 2018, 8:24am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/10 "2018-10-08T08:24:25Z")
What you show is important, but it is unrelated to random number generation. If you take any vector `x` (random or not) you will get the same result. What I understand @Tamas_Papp says is that `skewness(1.0 .- x) == skewness(x)` will be often false due to roundoff errors.
---
### Author:  [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)
#### Post date: [October 8, 2018, 8:25am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/11 "2018-10-08T08:25:54Z")
The swapping of signs in skewness is not a function of roundoff errors, it is a function of the mirroring.
---
### Author:  [@bkamins](https://discourse.julialang.org/u/bkamins)
#### Post date: [October 8, 2018, 8:26am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/12 "2018-10-08T08:26:02Z")
> [@JeffreySarnoff](#):
>
> Once that happens
This is correct - if you have a non-uniform distribution on `[0,1[` then taking `1` minus it might hit the non uniformity problem.
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [October 8, 2018, 8:27am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/13 "2018-10-08T08:27:15Z")
> [@JeffreySarnoff](#):
>
> I am demonstrating skewness in small random samples and that it swaps signs using `1.0 .- rand()`
No, as s(x) = -s(A-x) is an identity for s being `skewness`, and A a constant. What you are showing is that this does not hold in practice, because of numerical error. That is orthogonal to this discussion. Cf eg
```julia
julia> x = rand(10^9);
julia> A = 100
100
julia> sum(x) + A == sum(x .+ A)
false
```
and various similar examples.
---
### Author:  [@bkamins](https://discourse.julialang.org/u/bkamins)
#### Post date: [October 8, 2018, 8:28am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/14 "2018-10-08T08:28:06Z")
I am referring to:
```julia
julia> using Random
julia> Random.seed!(100);
julia> x = rand(100000);
julia> skewness(1.0 .- x) == -skewness(x)
false
```
and you see that the sign is swapped but the values are not exactly opposite - they are only approximately opposite.
---
### Author:  [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)
#### Post date: [October 8, 2018, 8:29am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/15 "2018-10-08T08:29:09Z")
this is getting away from itself – try the same thing using Float16 rands, Float16(skewness(x)) and 1000 samples. I know that floating point errors accrue – no argument there. 😉
_coding to the internal workings of rand() … kinda iffy for FAA system simulations_
---
### Author:  [@DNF](https://discourse.julialang.org/u/DNF)
#### Post date: [October 8, 2018, 10:57am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/16 "2018-10-08T10:57:58Z")
So you’re saying that if you take `1.0 - rand()` then many of the small floats, close to zero, can _never_ be selected, since `eps` is larger close to 1.0? Those small numbers just become inaccessible to the algorithm.
---
### Author:  [@bkamins](https://discourse.julialang.org/u/bkamins)
#### Post date: [October 8, 2018, 11:27am UTC](https://discourse.julialang.org/t/random-number-in-0-1/16009/17 "2018-10-08T11:27:02Z")
Yes. You can theoretically get `0` and the next theoretically possible value is `eps()`.