Define a more generic meaning for `typemin`/`typemax`

Internals & Design
1

typemin(T) says

The lowest value representable by the given (real) numeric DataType T.

Suppose we want to be more generic than a “(real) numeric” datatype. What should it say then?

How about

The minimum value representable by the given DataType having a unique minimum value.

2

one might think from the docstring that

typemin(::T)

returns value v such that

min(v, w) == v

for all w where typeof(w) <: T

however unfortunately this isn’t always true…

3

Could we use isless? Is this accurate?

The lowest value representable by the DataType T as ordered by [`isless`](@ref); this value isless than all other values of type T.

1 Like
4

it would have to be isless || isequal

5

What’s an example of a datatype with multiple equal typemin values?

6

Conversely, defining typemax as

The highest value representable by the DataType T as ordered by [isless](@ref); this value isless than no other values of type T.

seems obvious but breaks in the presence of NaN.

julia> isless(typemax(Float64), NaN)
true
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7

good point, nvm :grin:
was trying to construct something with subnormals but they don’t work like I thought

but still, it’s not true for DateTime as noticed by @Sukera `typemin`/`typemax` of `DateTime` is not actually the smallest/largest representable `DateTime` · Issue #50931 · JuliaLang/julia · GitHub

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8

I believe the proper predicate is typemax(T) means that !exists x such that isless(typemax(T), x)

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9 
julia> isless(typemax(Float64), NaN)
true

Can we say “… in the well ordered subset of values of T” or something like that?

10

Yes (I think that’s equivalent to what I wrote above, but it’s late). x = NaN exists anyways.