# Base.Inf for other Number types?

**URL:** <https://discourse.julialang.org/t/base-inf-for-other-number-types/45783>\
**Category:** New to Julia\
**Created:** [August 30, 2020, 8:02am UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783 "2020-08-30T08:02:08Z")\
**Posts on this page:** 10\
**Page:** 1

<div class="post-metadata">

**Author:** ![liuyxpp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/liuyxpp/32/9870_2.png) [@liuyxpp](https://discourse.julialang.org/u/liuyxpp)\
**Post date:** [August 30, 2020, 8:02am UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783/1 "2020-08-30T08:02:08Z")

</div>

Currently, it seems `Inf` is only defined for `Float*`. I am wondering if it possible to extend this to other data types, such as `Integer`? Then just like `zero` and `one`, we can have

```julia
julia> infinity(1.0)
Inf
julia> infinity(1)
# An `Inf` of type `Int`.

```

Currently, I mimic the behavior using `typemin` and `typemax`.

```julia
function infinity(::T) where T<:Real
    return typemax(T)
end

function isinfinity(n::T) where T<:Real
    return n == infinity(n)
end

```

Edited: I really have to narrow `Number` to `Real` since the infinity of `Complex` is undefined?

Edited 2: After read all suggestions, I come up following solution: just use a Union type. Thanks for all!

```julia
struct MyPhysParameter{T<:Real}
    value_type::T
    allowed_min::Union{T, typeof(Inf)}
    allowed_max::Union{T, typeof(Inf)}
end

```

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<div class="post-metadata">

**Author:** ![xiaodai](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/xiaodai/32/15937_2.png) [@xiaodai](https://discourse.julialang.org/u/xiaodai)\
**Post date:** [August 30, 2020, 8:20am UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783/2 "2020-08-30T08:20:04Z")

</div>

eh… I think the issue is that there isn’t an infinity defined in Int… the largest value is 2^63-1 with no spares.

I wonder what is the negative version of 0 for?

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<div class="post-metadata">

**Author:** ![liuyxpp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/liuyxpp/32/9870_2.png) [@liuyxpp](https://discourse.julialang.org/u/liuyxpp)\
**Post date:** [August 30, 2020, 8:48am UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783/3 "2020-08-30T08:48:59Z")

</div>

The `zero` and `one` in my post refer to `Base.zero` and `Base.one` which simply return 0 and 1 of the same type of the input argument. Examples:

```julia
julia> zero(-1.0)
0.0
julia> zero(-1)
0
julia> zero(1 - 2.0im)
0.0 + 0.0im

```

---

<div class="post-metadata">

**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [August 30, 2020, 10:25am UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783/4 "2020-08-30T10:25:11Z")

</div>

> [@liuyxpp](#):
>
> I am wondering if it possible to extend this to other data types, such as `Integer` ?

To `Integer`, _technically_ yes, since you can define

```julia
struct InfinityInteger <: Integer end
Base.isinfinite(::InfinityInteger) = true

```

etc, but not to `Int`, since that is a bits type that has no representation for infinity.

Practically, since you have to use at least `Union` types anyway, I would recommend you just use `Inf::Float64` or similar.

---

<div class="post-metadata">

**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [August 30, 2020, 10:25am UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783/5 "2020-08-30T10:25:55Z")

</div>

Alternatively, you can wrap `Int` and use sentinel values.

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<div class="post-metadata">

**Author:** ![cstjean](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cstjean/32/1444_2.png) [@cstjean](https://discourse.julialang.org/u/cstjean)\
**Post date:** [August 30, 2020, 10:39am UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783/6 "2020-08-30T10:39:47Z")

</div>

I would go for `Union{Int64, InfinityInteger}`. It’s cleaner, and `Union{Int64, Float64}` tends to get smushed over time:

```julia
julia> [1, Inf]
2-element Array{Float64,1}:
  1.0
 Inf

julia> identity.(Union{Int, Float64}[1, Inf])
2-element Array{Real,1}:
  1
 Inf

```

And there might be cases where it infers better.

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<div class="post-metadata">

**Author:** ![dlfivefifty](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dlfivefifty/32/1959_2.png) [@dlfivefifty](https://discourse.julialang.org/u/dlfivefifty)\
**Post date:** [August 30, 2020, 12:59pm UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783/7 "2020-08-30T12:59:23Z")

</div>

InfiniteArrays.jl has `Infinity <: Integer`. This is going to be moved to JuliaMath/Infinities.jl as `InfiniteCardinal{0}`

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<div class="post-metadata">

**Author:** ![tim.holy](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tim.holy/32/52_2.png) [@tim.holy](https://discourse.julialang.org/u/tim.holy)\
**Post date:** [August 30, 2020, 1:03pm UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783/8 "2020-08-30T13:03:21Z")

</div>

@Tamas_Papp’s answer and others proposing/implementing infinity types are a good ones.

If you want to avoid the `Union`…I started working on a `NaNIntegers` package, but never finished it. Here’s the start: [https://gist.github.com/timholy/569475b24763d1fbd36a42634192cb74](https://gist.github.com/timholy/569475b24763d1fbd36a42634192cb74). It uses the second-from-top-bit to indicate NaN. You could modify this to use the third-from-top-bit to indicate infinity. Note you have to write your own rules of mathematics, so there’s still a bit of work to do.

I’d generally recommend against mimicking infinity with `typemax`:

```julia
julia> i = typemax(Int)
9223372036854775807

julia> i+1 == i
false

julia> 2*i == i
false

julia> i-1 == i
false

```

Any infinity that doesn’t obey those properties is not really infinity.

---

<div class="post-metadata">

**Author:** ![liuyxpp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/liuyxpp/32/9870_2.png) [@liuyxpp](https://discourse.julialang.org/u/liuyxpp)\
**Post date:** [August 30, 2020, 1:24pm UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783/9 "2020-08-30T13:24:15Z")

</div>

Great suggestions. However, my usage of infinity is not as ambitious as yours. I only intend to use it as a indicator to mark the infinity, that is to say I will never do any math operations on it.

Here is what I want to do. I want to define a type which describes a physical parameter. Now, with this type I can dispatch some physical computation on it.

```julia
struct MyPhysParameter{T<:Real}
    description::String
    variable_name::String
    ascii_label::String
    allowed_min::T # the minimum value allowed for this parameter, can be negative infinity
    allowed_max::T # the maximum value allowed for this parameter, can be positive infinity
end

```

So I will need a type stable way to define the infinity.

Typical dispatch case

```julia
function compute(::MyPhysParameter, data)
    # use the bounds to `rand` or check data validity, etc.
end

```

---

<div class="post-metadata">

**Author:** ![tim.holy](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tim.holy/32/52_2.png) [@tim.holy](https://discourse.julialang.org/u/tim.holy)\
**Post date:** [August 30, 2020, 1:42pm UTC](https://discourse.julialang.org/t/base-inf-for-other-number-types/45783/10 "2020-08-30T13:42:51Z")

</div>

If you want to encode the min/max, why not just use `typemin`/`typemax`?

Edit:

> I only intend to use it as a indicator to mark the infinity, that is to say I will never do any math operations on it.

The problem I foresee with calling this `Inf` is, what happens when you come back to this after six months away and then forget that you can’t do math operations on it? Calling it `Inf` is a slippery slope…