I recently ran into an issue overriding zero for my own Number: julia> immutable Infinity <: Number end julia> Base.zero(::Infinity) = 0 julia> import Base: + julia> +(::Infinity,::Int) = Infinity() + (generic function with 181 methods) julia> reduce(+,[Infinity(),Infinity()]) ERROR: MethodErro…

[image] dlfivefifty: The issue appears to be that zero{T<:Number}(::T) is expected to return a T. Is this a bug, or is this part of the Number “Interface”? Is the Number “Interface” written down anywhere? I’d say it’s part of the interface. If you can’t expect that zero(::T) returns a type…

OK that’s reasonable. Yes, if built in types have an interface that Base Julia assumes (like for Number) it should be written down. Even better, there should be a testnumberinterface(Infinity) to test that all the contracts that Base expects are satisfied for my type. (Also, testiterator, testabs…

[image] dlfivefifty: The issue appears to be that zero{T<:Number}(::T) is expected to return a T. Is this new in v0.6? For v0.5, the following works: immutable Infinity <: Number end Base.zero(::Infinity) = 0 import Base: + +(::Infinity,::Int) = Infinity() +(::Infinity,::Infinity) = Infin…

Yes it’s 0.6 (sorrry, should have mentioned this was a surprising new behaviour of something that worked fine in 0.5)

Note that the precise problem is not that zero() returns a different type, it’s that the value returned by zero() cannot be converted to Infinity. Defining this (incorrect) method fixes the issue: Base.convert(::Type{Infinity}, x::Integer) = Infinity(). This sounds like an unintentional restrictio…

Created an issue: https://github.com/JuliaLang/julia/issues/21097

I was suggested this topic when I was about to start a new development discussion titled “What is a Number” In general, interfaces and abstract types in Julia are pretty well documented and defined, (e.g. AbstractArray, iterator interface, …). It is suprising to see so little documentation about wh…

I run into a related problem frequently: if I get a container with element type T <: Number, and create a result S, which I need to precompute, what is the best way to do this? Think of T eg as a ForwardDiff.Dual, or a similar construct related to a tape from one of the reverse AD packages. Eg if I…

So first the mathematics This is the wrong approach I think. I doubt there’s any useful mathematical definition that includes everything that needs to be <: Number, e.g., floating point arithmetic, interval arithmetic, quaternions, dual numbers, etc. It’s much better to define Number as an inter…

Yes I was exaggerating, I know it’s not a good idea to try to map mathematical structures onto the type hierarchy for various reasons. But I do mean establishing the kind of mathematical properties that are expected of a Number, i.e. I guess commutative addition operator, associative but not necessa…

Interface for `Number`

General Usage

Tamas_Papp January 11, 2019, 5:48pm 16

Which is why existing best practices should be shared, possibly in a package.

Overview of different number representations, philosophies and use cases

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Interface for `Number`

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