# Instancing a custom number type and using in arrays

**URL:** <https://discourse.julialang.org/t/instancing-a-custom-number-type-and-using-in-arrays/34071>\
**Category:** New to Julia\
**Created:** [February 2, 2020, 1:05am UTC](https://discourse.julialang.org/t/instancing-a-custom-number-type-and-using-in-arrays/34071 "2020-02-02T01:05:59Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![GregVernon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gregvernon/32/5611_2.png) [@GregVernon](https://discourse.julialang.org/u/GregVernon)\
**Post date:** [February 2, 2020, 1:05am UTC](https://discourse.julialang.org/t/instancing-a-custom-number-type-and-using-in-arrays/34071/1 "2020-02-02T01:05:59Z")

</div>

I’m trying to write FEM code for school and I’d like to use custom number types as a means of error-proofing. Essentially, I’d like to have a type difference between element ids, global node ids, local node ids, global dof ids, local dof ids, etc. Then arrays of these entries would be something like

```julia
elem_connectivity = Array{elem_id,2}(undef, num_local_nodes, num_elems)

```

etc. and it would be impossible to put the wrong kind of number in them. Additionally, I would like to make indexing the arrays require the right type of number, e.g

```julia
elem_connectivity[a::loc_node_id, e::elem_id] 

```

I’ve tried reading the manual on primitive types, but I seem to be unsure of how to begin creating instances of the types I create. For example

```julia
primitive type nodeID <: Signed 64 end
a = nodeID(100)

ERROR: MethodError: no method matching nodeID(::Int64)
Closest candidates are:
  nodeID(::T) where T<:Number at boot.jl:718
  nodeID(::Float16) where T<:Integer at float.jl:71
  nodeID(::Complex) where T<:Real at complex.jl:37
  ...
Stacktrace:
 [1] top-level scope at REPL[10]:1

```

Thoughts?

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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:** [February 2, 2020, 2:54am UTC](https://discourse.julialang.org/t/instancing-a-custom-number-type-and-using-in-arrays/34071/2 "2020-02-02T02:54:18Z")

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```julia
julia> primitive type nodeID 64 end

julia> nodeID(i::Integer) = reinterpret(nodeID, Int64(i))
nodeID

julia> nodeID(30)
nodeID(0x000000000000001e)

```

(If you’re not going to define arithmetic operations on it, don’t make it a subtype of `Signed`.)

But honestly, it sounds like your plan for a distinct type for each kind of index involves a lot of pain, little gain, and will result in non-idiomatic Julia code.

---

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**Author:** ![JeffreySarnoff](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jeffreysarnoff/32/1980_2.png) [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)\
**Post date:** [February 2, 2020, 3:00am UTC](https://discourse.julialang.org/t/instancing-a-custom-number-type-and-using-in-arrays/34071/3 "2020-02-02T03:00:31Z")

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For your purposes, using `struct` types rather than `primitive` types makes the task easier and codes more concisely. To simplify your specifics (for clarity) there should be types `ElementId`, `GlobalNodeId`, `LocalNodeId`. Each of these should subtype `Signed` and otherwise behave as an `Int`.

This is elaborated code to help you see how to do this with `structs`; for example, you may not need abstract types beyond `AbstractId`.

```julia
abstract type AbstractId <: Signed end
abstract type AbstractNodeId <: AbstractId end
abstract type AbstractElementId <: AbstractId end

struct ElementId <: AbstractElementId
  id::Int
end

struct GlobalNodeId <: AbstractNodeId
  id::Int
end

struct LocalNodeId <: AbstractNodeId
  id::Int
end

# so values of these types display just as an Int does
for T in (:ElementId, :GlobalNodeId, LocalNodeId)
    @eval begin
         Base.show(io::IO, x::$T) = show(io, x.id)
    end
end

# to create concrete ids of each type, all valued `1`
element_id = ElementId(1)
global_node_id = GlobalNodeId(1)
local_node_id = LocalNodeId(1)

```

You may have questions about what next / how to use these types to do \_ .  
Ask away. If you want to compare two ids of the same type those comparison operations need to be defined for each `struct` type.

```julia
import Base: <. <=, ==
for Op in (:(<). :(<=), :(==),)
    @eval begin
         $Op(x::ElementId, y::ElementId) = $Op(x.id, y.id)
         $Op(x::GlobalNodeId, y::GlobalNodeId) = $Op(x.id, y.id)
         $Op(x::LocalNodeId, y::LocalNodeId) = $Op(x.id, y.id)
    end
end

```

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<div class="post-metadata">

**Author:** ![GregVernon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gregvernon/32/5611_2.png) [@GregVernon](https://discourse.julialang.org/u/GregVernon)\
**Post date:** [February 2, 2020, 3:13am UTC](https://discourse.julialang.org/t/instancing-a-custom-number-type-and-using-in-arrays/34071/4 "2020-02-02T03:13:26Z")

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I’m ready for the pain - my advisor’s startup is developing an FEM code in C++ and what I described is how they’ve developed their code. I’m trying to follow this approach as much as possible in Julia. Sadly I don’t have access to their source so I don’t know _exactly_ what they’re doing in C++. That being said, I’ll probably follow @JeffreySarnoff’s approach instead, because that seems a lot less painful.

---

<div class="post-metadata">

**Author:** ![GregVernon](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gregvernon/32/5611_2.png) [@GregVernon](https://discourse.julialang.org/u/GregVernon)\
**Post date:** [February 2, 2020, 3:15am UTC](https://discourse.julialang.org/t/instancing-a-custom-number-type-and-using-in-arrays/34071/5 "2020-02-02T03:15:52Z")

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@JeffreySarnoff I’m going to accept this as the solution to the question as posed, but I will probably take you up on your suggestion to _ask away_. I’m going to stew on / experiment with what you’ve described and will reply with any further questions.

---

<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:** [February 2, 2020, 5:54pm UTC](https://discourse.julialang.org/t/instancing-a-custom-number-type-and-using-in-arrays/34071/6 "2020-02-02T17:54:06Z")

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> [@GregVernon](#):
>
> my advisor’s startup is developing an FEM code in C++ and what I described is how they’ve developed their code

It’s great that you have an existing FEM code to guide you in your choice of algorithms. However, realize that Julia and C++ are _very_ different languages, and the choice of abstractions and code structure in C++ may not be a good template for a Julia implementation.