# Julian way of defining custom numeric types
**URL:** https://discourse.julialang.org/t/julian-way-of-defining-custom-numeric-types/53866
**Category:** New to Julia
**Created:** [January 24, 2021, 4:50pm UTC](https://discourse.julialang.org/t/julian-way-of-defining-custom-numeric-types/53866 "2021-01-24T16:50:22Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@cshen](https://discourse.julialang.org/u/cshen)
#### Post date: [January 24, 2021, 4:50pm UTC](https://discourse.julialang.org/t/julian-way-of-defining-custom-numeric-types/53866/1 "2021-01-24T16:50:22Z")
Hello,
I am working with the DifferentialEquations package to play around some differential equations involving angles.
Instead of letting everything go on as a normal float and just afterwards reduce everything modulo 2pi for visualisation, i wanted to try to go the julian way and define a small wrapper for the Floag64 type
```julia
struct Angle <: Real
x::Float64
end
Angle(x::Real) = Angle(x % 2pi)
```
Unfortunately this is not enough to make for a smooth addition to my program as julia struggles to convert and does not know what to do with this new type.
I know that i can extend all the base operations by hand, but i was left wondering if there is a smoother and easier way to let a simple primitive Number type wrapper just automatically fall in place the rest of the Julia implementation.
More in general i tried to look for some quick guidelines when creating a new custom type but i could not find one. Are there any Best Practices ™ when it comes to seamlessly embed a new custom type in the language?
Thanks!
---
### Author:  [@Tomas\_Pevny](https://discourse.julialang.org/u/Tomas_Pevny)
#### Post date: [January 24, 2021, 5:24pm UTC](https://discourse.julialang.org/t/julian-way-of-defining-custom-numeric-types/53866/2 "2021-01-24T17:24:35Z")
You should find an inspiration in manual describing the implementation of rational number.
[https://docs.julialang.org/en/v1/manual/conversion-and-promotion/](https://docs.julialang.org/en/v1/manual/conversion-and-promotion/)
---
### Author:  [@Henrique\_Becker](https://discourse.julialang.org/u/Henrique_Becker)
#### Post date: [January 24, 2021, 5:28pm UTC](https://discourse.julialang.org/t/julian-way-of-defining-custom-numeric-types/53866/3 "2021-01-24T17:28:42Z")
Also, I think you can benefit from the macro `@forward` that I describe in [this reply of mine](https://discourse.julialang.org/t/confused-with-type-definition/53115/13).
---
### Author:  [@cshen](https://discourse.julialang.org/u/cshen)
#### Post date: [January 24, 2021, 5:51pm UTC](https://discourse.julialang.org/t/julian-way-of-defining-custom-numeric-types/53866/4 "2021-01-24T17:51:34Z")
This is extremely interesting but the `@forward` macro seems to not retain the type as in
```julia
struct Angle <: Real
x::Float64
end
@forward Angle.x Base.sqrt
```
then
```julia
typeof(Base.sqrt(Angle(1))) == Float64 #true
```
and that is not really what i need. Moreover, using forward on `Base.:+` raises a `MethodError` anyway as there is ambiguity as the macro defines
```julia
+(x::Angle, args...; kwargs...)
```
I think i’ll stick the the “not lazy” version of embedding a custom type for now.
---
### Author:  [@Henrique\_Becker](https://discourse.julialang.org/u/Henrique_Becker)
#### Post date: [January 24, 2021, 6:08pm UTC](https://discourse.julialang.org/t/julian-way-of-defining-custom-numeric-types/53866/5 "2021-01-24T18:08:03Z")
True, maybe `eval` would be more the case here.
```julia
for single_param_function in (:(Base.sqrt), :(Base.sin))
eval(quote
function $(single_param_function)(a :: Angle)
return Angle($(single_param_function)(a.x))
end
end)
end
```
Someone with better knowledge of metaprogramming should check if this is reasonable (it works, but maybe is not ideal).
---
### Author:  [@sostock](https://discourse.julialang.org/u/sostock)
#### Post date: [January 24, 2021, 7:28pm UTC](https://discourse.julialang.org/t/julian-way-of-defining-custom-numeric-types/53866/6 "2021-01-24T19:28:10Z")
> [@cshen](#):
>
> `Angle(x::Real) = Angle(x % 2pi)`
Note that you will get more accurate results by using `mod2pi(x)` instead of `x % 2pi` (since the latter uses `2pi`, a `Float64` approximation of the actual number 2π).
---
### Author:  [@Per](https://discourse.julialang.org/u/Per)
#### Post date: [January 25, 2021, 7:10am UTC](https://discourse.julialang.org/t/julian-way-of-defining-custom-numeric-types/53866/7 "2021-01-25T07:10:42Z")
Is the sine of an angle another angle or just a number? If you don’t need it to be an angle, then simply defining `Base.float` for your type will work for a lot of functions that use this as their fallback.
```julia
julia> Base.float(a::Angle) = a.x
julia> sin(Angle(1))
0.8414709848078965
```