Does `fastabs(z::Complex)` mean something different than faster computation of `abs(z::Complex)`?

[chenspc]

I came across the fastabs function here in SpecialFunctions.jl and here in Base.Math. I'm confused by its definition.

julia> z = 3 + 4im
3 + 4im

julia> abs(z)
5.0

julia> Base.Math.fastabs(z)
7

Shouldn't it be something like below?

julia> fastabs(z::Complex) = √(abs2(real(z)) + abs2(imag(z)))
fastabs (generic function with 1 method)

julia> fastabs(z)
5.0

Or does it mean something else?

[Roger-luo]

according to docs

Faster abs-like function for rough magnitude comparisons. fastabs is
equivalent to abs(x) for most x, but for complex x it computes
abs(real(x))+abs(imag(x)) rather than requiring hypot.

where hypot is implemented as

Compute the hypotenuse \sqrt{|x|^2+|y|^2} avoiding overflow and underflow.

This code is an implementation of the algorithm described in: An Improved
Algorithm for hypot(a,b) by Carlos F. Borges The article is available online
at ArXiv at the link https://arxiv.org/abs/1904.09481

[oscardssmith]

Note that if this was an issue, it would be an issue with SpecialFunctions.jl not Base.

[chenspc]

Sorry, but my question wasn't about the implementation or speed, it's the value of fastabs(3+4im) gives 7 rather than 5.

@oscardssmith In SpecialFunctions.jl, it seems that the author plan to use the fastabs from the Base.Math in the near future. My concern is that this is a bug in both places.

[oscardssmith]

This isn't a bug. It's intended behavior. It provides something meant for internal use only with the documented behavior.

[chenspc]

I'm not sure what this intended behaviour is but I guess that's a question for discourse. In the document, it says

...rather than requiring hypot.

which seems to suggest it would give the same result (hypot(3+4im) gives 5) just not calling the it.

[oscardssmith]

I think

for complex x it computes abs(real(x))+abs(imag(x))

makes it pretty clear what it's supposed to do. If there's a way to make this clearer we might consider it, but we aren't changing the behavior of the function.