# Unexpected Behaviour of the Rounding Function

**URL:** <https://discourse.julialang.org/t/unexpected-behaviour-of-the-rounding-function/79101>\
**Category:** General Usage\
**Created:** [April 6, 2022, 2:02pm UTC](https://discourse.julialang.org/t/unexpected-behaviour-of-the-rounding-function/79101 "2022-04-06T14:02:08Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![GrandlyHelping](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/grandlyhelping/32/35257_2.png) [@GrandlyHelping](https://discourse.julialang.org/u/GrandlyHelping)\
**Post date:** [April 6, 2022, 2:02pm UTC](https://discourse.julialang.org/t/unexpected-behaviour-of-the-rounding-function/79101/1 "2022-04-06T14:02:08Z")

</div>

I am trying to round some Float64 values and don’t understand the behavior of the round() function for specific values.

If I take:

round(0.585, digits=2, RoundNearestTiesUp)

I get 0.59, as expected, since I want values to be rounded up when ending in a 5.

However, for:

round(0.575, digits=2, RoundNearestTiesUp)

I get 0.57, which I don’t understand. This goes for 0.565 as well for some reason.

My question is why does this happen, particularly when I get the expected behavior for 0.505,0.515…0.595, except for 0.565 and 0.575?

I assume this has to do with the RoundingMode, but does anyone have any suggestions as to how I can consistently get the appropriate rounding of Float64s that I’m looking for; a work around perhaps?

PS:

I’m using Julia version 1.7.1

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<div class="post-metadata">

**Author:** ![Oscar\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/oscar_smith/32/25343_2.png) [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)\
**Post date:** [April 6, 2022, 2:09pm UTC](https://discourse.julialang.org/t/unexpected-behaviour-of-the-rounding-function/79101/2 "2022-04-06T14:09:21Z")

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Floating point numbers aren’t decimal.

```julia
julia> big(0.575)
0.5749999999999999555910790149937383830547332763671875

```

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<div class="post-metadata">

**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [April 6, 2022, 2:10pm UTC](https://discourse.julialang.org/t/unexpected-behaviour-of-the-rounding-function/79101/3 "2022-04-06T14:10:28Z")

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> [@GrandlyHelping](#):
>
> `round(0.575, digits=2, RoundNearestTiesUp)`
> 
> I get 0.57, which I don’t understand. This goes for 0.565 as well for some reason.

I think that’s because the decimal value `0.575` is not exactly represented in binary floating-point arithmetic. It’s actually the value:

```julia
julia> big(0.575)
0.5749999999999999555910790149937383830547332763671875

```

which is `< 0.575`:

```julia
julia> 0.575 < 575//1000
true

```

so it correctly rounds down to `0.57`. See [PSA: floating-point arithmetic](https://discourse.julialang.org/t/psa-floating-point-arithmetic/8678)

The surprising thing to me is that `0.585` rounds up, since we also have:

```julia
julia> big(0.585)
0.58499999999999996447286321199499070644378662109375

julia> 0.585 < 585//1000
true

```

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<div class="post-metadata">

**Author:** ![Oscar\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/oscar_smith/32/25343_2.png) [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)\
**Post date:** [April 6, 2022, 2:13pm UTC](https://discourse.julialang.org/t/unexpected-behaviour-of-the-rounding-function/79101/4 "2022-04-06T14:13:37Z")

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I think what’s happening here is that `.58` and `.59` are both slightly less than their decimal values as well (but I’m not 100% sure here)

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<div class="post-metadata">

**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [April 6, 2022, 2:17pm UTC](https://discourse.julialang.org/t/unexpected-behaviour-of-the-rounding-function/79101/5 "2022-04-06T14:17:08Z")

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Note that if you want to work with decimal values exactly you can use [decimal floating point](https://github.com/JuliaMath/DecFP.jl):

```julia
julia> using DecFP

julia> round(d"0.575", digits=2, RoundNearestTiesUp)
0.58

julia> round(d"0.585", digits=2, RoundNearestTiesUp)
0.59

```

It’s rare to actually _need_ this in a real application, but it does make human interpretation of decimal inputs and outputs easier.

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<div class="post-metadata">

**Author:** ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)\
**Post date:** [April 6, 2022, 2:24pm UTC](https://discourse.julialang.org/t/unexpected-behaviour-of-the-rounding-function/79101/6 "2022-04-06T14:24:14Z")

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> [@Oscar\_Smith](#):
>
> I think what’s happening here is that `.58` and `.59` are both slightly less than their decimal values as well (but I’m not 100% sure here)

`Float64(0.585)` is exactly halfway between `Float64(0.58)` and `Float64(0.59)`. However, the same is true for `Float64(0.575)`, which is exactly halfway between `Float64(0.57)` and `Float64(0.58)`:

```julia
julia> big(0.59) - big(0.585)
0.00500000000000000444089209850062616169452667236328125

julia> big(0.585) - big(0.58)
0.00500000000000000444089209850062616169452667236328125

julia> big(0.58) - big(0.575)
0.00500000000000000444089209850062616169452667236328125

julia> big(0.575) - big(0.57)
0.00500000000000000444089209850062616169452667236328125

```

So, by this logic, shouldn’t `0.575` also round up to `0.58`?

Probably there is an additional roundoff error in the `round` code…

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<div class="post-metadata">

**Author:** ![GrandlyHelping](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/grandlyhelping/32/35257_2.png) [@GrandlyHelping](https://discourse.julialang.org/u/GrandlyHelping)\
**Post date:** [April 6, 2022, 3:53pm UTC](https://discourse.julialang.org/t/unexpected-behaviour-of-the-rounding-function/79101/7 "2022-04-06T15:53:18Z")

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Thank you for your recommendation, I’ll check out the DecFP.jl package.

---

<div class="post-metadata">

**Author:** ![GrandlyHelping](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/grandlyhelping/32/35257_2.png) [@GrandlyHelping](https://discourse.julialang.org/u/GrandlyHelping)\
**Post date:** [April 6, 2022, 4:02pm UTC](https://discourse.julialang.org/t/unexpected-behaviour-of-the-rounding-function/79101/8 "2022-04-06T16:02:29Z")

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Well, strangely, it might not be as rare in real application.

In my case, I was trying to verify a min-max normalization on a fairly large data-set of around 42000 entries. I used DataFrames’ transform function to apply the calculation and rounding of the result across each value in the DataFrame.

And since, I already have a normalized version of the data (I was just checking them), I found some inaccuracies in comparing my results and to those of the pre-normalized data.

With that said, unexpected rounding was on average extremely infrequent. Nevertheless, I could see decimal floating point having a place in data manipulations that require a great deal of accuracy.