`mean` of fixed-point numbers is a `Float64`

[jariji]

using Statistics, FixedPointNumbers

julia> typeof(mean([(N0f8(.5)), (N0f8(.5))]))
Float64

Is this the intended behavior? I expected it would round to the nearest fixed-point number.

[kimikage]

At least that is the behavior @timholy intended.
cf. #183, JuliaStats/Statistics.jl#165 (comment)

This is consistent with the default behavior of integer types.

julia> typeof(mean([0x80, 0x80]))
Float64

Also, while N0f8 is used for image processing, Float32 is not always accurate enough.

[kimikage]

Note that it is not a good idea to use Float32 for the N0f8 value accumulations. N24f8 is superior in both speed and accuracy.

[jariji]

@timholy Can I ask the rationale for this behavior?

• I thought the point of a fixed-point type was to preserve the type by rounding, but that's not what I see here.
• I thought sum(_) and reduce(+, _) were supposed to return the same.

julia> N0f8(.5) + N0f8(.5) |> typeof
N0f8 (alias for Normed{UInt8, 8})

julia> reduce(+, [N0f8(.5), N0f8(.5)]) |> typeof
N0f8 (alias for Normed{UInt8, 8})

julia> sum([N0f8(.5), N0f8(.5)]) |> typeof
Float64

julia> N0f8(1)/2 |> typeof
Float32

[kimikage]

As implied above, UInt8 is a counterexample to your expectation.

julia> 0x80 + 0x80 |> typeof
UInt8

julia> reduce(+, [0x80, 0x80]) |> typeof
UInt8

julia> sum([0x80, 0x80]) |> typeof
UInt64

julia> 0xff/2 |> typeof
Float64

Of course, since fixed-point numbers are different from both integers and floating-point numbers, this package can and shall design its own rules. And, there is already a design.
In other words, I think it is you who must provide the "objective" rationale.

[kimikage]

I am planning to change the design once Statistics.jl provides a richer public API.
However, I think the return types will remain as they are.