Julia: `sign(pi)` errors

[Moelf]

Didn't find an existing issue

julia> sign(pi)
ERROR: InexactError: Bool(-1)

https://discourse.julialang.org/t/problem-with-sign-pi/47801/

[JeffBezanson]

What type should it return? Float64?

[Moelf]

that's the real question. I would say Float64 since if one is using a Real number probably they are not dealing with integers in the rest of the expression anyways. (reason why 3 * pi gives Float64)

or Int8 for minimal promotion. But that can be weird at first glance. (but at the same time, one(pi) = true already....)

[PallHaraldsson]

Can you fix this with:

julia> import Base.sign

julia> sign(:Irrational{:π}) = true

i.e. why not with Bool?

I tried to fix for all (only two?) such constants, and all future ones:

julia> Revise.track(Base)

julia> sign(AbstractIrrational) = true
┌ Error: Failed to revise /home/pharaldsson_sym/julia-1.6-a0a68a54d6/share/julia/base/Base.jl

without the Revise command it ran, while ineffective, since Real is checked first? It there no way for it to be checked later?

[Moelf]

@PallHaraldsson you mean:

julia> sign(::AbstractIrrational) = true
sign (generic function with 10 methods)

There are a few of them.

yeah, that could work actually, since there's no way to represent a negative Irrational in the first place (they are just Symbols under the hood)

[simeonschaub]

What type should it return? Float64?

Since signed(true) returns an Int, that seems like the most intuitive answer to me.

@Moelf AbstractIrrationals are also defined by packages like Tau.jl, so I don't think it's safe to assume that an AbstractIrrational is always positive.

[Moelf]

@simeonschaub I see. that's true, but in terms of Julia's representation, we can't really represent a negative irrational number. -irr will send it to Float64.

[simeonschaub]

I am not sure I follow. For example, you can do the following:

julia> Base.@irrational negpi -3.141592653589793 -big(pi)

julia> negpi
negpi = -3.141592653589...

[Moelf]

I'm saying that:

julia> dump(-3//5)
Rational{Int64}
  num: Int64 -3
  den: Int64 5

the sign is encoded in num, but the irrational number are "just" symbols. But yes, I agree that hack fix may introduce hidden bugs. So an all-around approach is to take the sign of the Float64 representation of that irrational number.

[petvana]

As a user, I would expect that the following test is satisfied for any type (except for unsigned ones, obviously).

@test sign(pi) === -sign(-pi)

(Otherwise, I may cause unexpected type instability.)

[PallHaraldsson]

Is this also bad? I'm just not sure:

julia> one(pi) === one(-pi)  # and similarily for zero(pi) === zero(-pi)  and sign(pi) === one(pi)
false

[Moelf]

more reason to make everything about irrational just Float64 because of:

-(x::AbstractIrrational) = -Float64(x)

[petvana]

This is also counterintuitive.

julia> pi == one(pi) * pi
false

julia> zero(pi) == one(pi) * pi - pi
true

[PallHaraldsson]

The former is probably by design. Note:

julia> pi ≈ one(pi)*pi
true

julia> big(1.0)*pi
3.141592653589793238462643383279502884197169399375105820974944592307816406286198

julia> big(1.0)*pi == pi  # only in some CAS where 1.0 isn't Float converting pi to any finite Float, would this be the same.
false

[petvana]

The former is probably by design. Note:

I have found in docs of one()

Return a multiplicative identity for `x`: a value such that
`one(x)*x == x*one(x) == x`.

So I have opened a separate issue for that.

[StefanKarpinski]

The only solutions to most of these complaints are to delete the Irrational type entirely or to turn it into a full blown symbolic system. These things are only meant to allow you to use pi with different precisions easily, not to do computer algebra.

[oscardssmith]

So what you're saying is that the only 1.0 compatible fix is adding a basic CAS? Should good to me :)