trig functions are not type-stable for complex inputs

[waldyrious]

Came across this while working to improve test coverage:

julia> show(Base.return_types(sintau, Tuple{Complex}))
Any[Any]

julia> show(Base.return_types(costau, Tuple{Complex}))
Any[Any]

julia> show(Base.return_types(modtau, Tuple{Complex}))
Any[Any]

[waldyrious]

julia> sintau(convert(Int,1.0)) === zero(Int)
true

julia> sintau(convert(Float64,1.0)) === zero(Float64)
true

julia> sintau(convert(Complex,1.0)) === zero(Complex)
false

[waldyrious]

Note: this may be helped by JuliaLang/julia#20268

[giordano]

I don't think this is an issue:

julia> show(Base.return_types(sintau, Tuple{Complex{Float64}}))
Any[Complex{Float64}]

In addition, in PR #19 I used @inferred in new tests, that takes care of testing type stability of the result.

[waldyrious]

Before going further, I'd like to make sure you're aware of the context of my role in this package. I am currently maintaining it due to my interest in both Julia and tau, and the original author's lack of availability to maintain the package. However, my experience programming Julia is rather superficial, so I probably won't be able to communicate with you via code snippets alone :) -- and I'll likely ask some silly questions, so bear with me.

With that said, I must say I don't completely follow what you mean with your comment above. I'd appreciate if you could expand a bit.

[giordano]

Ok, don't worry ;-)

I don't know exactly what Base.return_types is supposed to do, it isn't documented, I can only guess based on its name. I simply showed that using Complex{Float64} as input type (that is, a Complex object with the parameter explicitly specified), the test is fine (and I added such test at https://github.com/JuliaMath/Tau.jl/pull/19/files#diff-fce720c43af3c52c862fd7451c7374b8R53). Instead, you were using Complex without specifying the parameter, that is the collection of all Complex types, and you can't infer a single returned type for all these input types.

In addition, in the same PR I used everywhere @inferred, which is very useful to test type stability of the given expression. If the function wrapped by @inferred isn't type-stable, an error is raised.

In the end, I believe this issue can be closed, as it isn't an issue at all ;-)

[waldyrious]

Thanks for the details! I had never really studied how Complex works at sufficient detail, which caused my confusion. I assumed it was a straightforward concrete type like Int, while indeed it is more of a container type (like an array of numbers, I suppose).

To confirm that I got this right: the correct form of the Complex test in the second above would be

julia> sintau(convert(Complex,1.0)) === zero(Complex{Float64})
true

right?

In any case, yes, let's close this.

[giordano]

Exact! Indeed

julia> zero(Complex)
0 + 0im

julia> typeof(ans)
Complex{Int64}

julia> sintau(one(Complex))
0.0 + 0.0im

julia> typeof(ans)
Complex{Float64}

Thus, sintau(one(Complex)) and zero(Complex) have different types, and === (which tests perfect equality) necessarily returns false.