_fill_dot support general vectors

[putianyi889]

including Inf, NaN and nested arrays. Infinite cases should be implemented in InfiniteArrays.jl

Original PR:

including Fill(0,∞) and potentially 0.0:0.0:+∞ in the future

also fix a type issue:

julia> dot(fill(true, 5), fill(Int8(1), 5)) |> typeof
Int8

julia> dot(sum(fill(true, 5)), Int8(1)) |> typeof
Int64

[codecov]

Codecov Report

Merging #229 (4c630e0) into master (dc8aa6e) will increase coverage by 0.14%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #229      +/-   ##
==========================================
+ Coverage   99.04%   99.19%   +0.14%     
==========================================
  Files           4        4              
  Lines         630      622       -8     
==========================================
- Hits          624      617       -7     
+ Misses          6        5       -1     

Impacted Files	Coverage Δ
src/fillalgebra.jl	99.42% <100.00%> (+0.52%)	⬆️

... and 1 file with indirect coverage changes

📣 We’re building smart automated test selection to slash your CI/CD build times. Learn more

[putianyi889]

Using sum(a)*value(b) can have rounding-off inconsistency as well as type instability. Somehow

julia> sum(fill(Int8(1),5)) |> typeof
Int64

julia> reduce(+, fill(Int8(1),5)) |> typeof
Int8

reduce doesn't work with ranges however.

[putianyi889]

Julia intentionally let sum not always return the same type. The reason is for "type stability" according to them.

https://github.com/JuliaLang/julia/blob/38d24e574caab20529a61a6f7444c9e473724ccc/base/reduce.jl#L390-L412

[putianyi889]

I'm accepting the rounding-off errors (See failed test) since I don't know how to work around. I tend to believe the default dot has larger errors.

[jishnub]

Checking for iszero(b) in the short-circuiting branch is O(n), so we might as well compute the sum?

[putianyi889]

I've found another problem...

For infinite vectors, if one of them is zero and another is well-defined, then the dot of them is zero.

However, if the other vector has Inf or NaN, we do want the dot to be NaN. This is a must-achieve for finite cases.

Most of the issues can be resolved by adding if-elses. The hard part is to tell whether an infinite vector with infinite sum actually contains Inf. I'm ignoring the last edge case for now.

The infinite case is also not type-stable, since the result could easily be ℵ₀. Maybe this should be done by InfiniteArrays.jl. @dlfivefifty any opinion?

[putianyi889]

sorry for the ping, inferred 😅

[dlfivefifty]

Is this Ready to merge?

[putianyi889]

yes