[RFC] Improve consistency of arithmetic with Bool

[kimikage]

I'm going to create some separate PRs for the parts not related to Bool.
This PR only fixes return types which are clearly unreasonable. Other inconsistent return types are leaved for backward compatibility for now.

I feel the need to make the code more generalized before we can achieve v1.0. However, I am not sure when to do that. (Edit: see #156)
Mostly improved.

[codecov]

Codecov Report

Merging #153 (19551e6) into master (32373c7) will increase coverage by 0.31%.
The diff coverage is 90.90%.

@@            Coverage Diff             @@
##           master     #153      +/-   ##
==========================================
+ Coverage   84.97%   85.29%   +0.31%     
==========================================
  Files           2        2              
  Lines         213      238      +25     
==========================================
+ Hits          181      203      +22     
- Misses         32       35       +3     

Impacted Files	Coverage Δ
src/ColorVectorSpace.jl	89.82% <90.90%> (-0.23%)	⬇️

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[kimikage]

v0.9.4

+	Bool	N0f8	Int64	Float32	Float64
Gray{Bool}	Gray{N0f8}🍇	Gray{N0f8}	Gray{N0f8}🍇	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float32}	Gray{Float64}
Gray24	Gray24	Gray24	Gray24🍇	Gray24🍇	Gray24🍇
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

+	Gray{Bool}	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Bool}	Gray{Bool}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

*	Bool	N0f8	Int64	Float32	Float64
Gray{Bool}	Gray{Float32}❌	Gray{N0f8}	Gray{BigFloat}❌	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}🍇	Gray{N0f8}🍇	Gray{Float32}	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

*	Gray{Bool}	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Bool}	Gray{Float32}❌	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

/	Bool	N0f8	Int64	Float32	Float64
Gray{Bool}	Gray{Float64}❌	Gray{N0f8}🍇	Gray{Float64}❌	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}🍇	Gray{N0f8}	Gray{Float32}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}🍇	Gray{N0f8}🍇	Gray{Float32}	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

/	Gray{Bool}	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Bool}	Gray{Float64}❌	Gray{N0f8}🍇	Gray{N0f8}🍇	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}🍇	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}🍇	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

(Added) /	Gray{Bool}	Gray{N0f8}	Gray24	Gray{Float32}
Bool	Gray{Float64}❌	Gray{N0f8}🍇	Gray24🍇	Gray{Float32}
N0f8	Gray{N0f8}🍇	Gray{N0f8}	Gray24	Gray{Float32}
Int64	Gray{Float64}❌	Gray{Float32}	Gray24🍇	Gray{Float32}
Float32	Gray{Float32}	Gray{Float32}	Gray24🍇	Gray{Float32}
Float64	Gray{Float64}	Gray{Float64}	Gray24🍇	Gray{Float64}

(Added) ^	Bool	Int64	Float32	Float64
Gray{Bool}	Gray{Float32}❌	Gray{Float32}❌	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}🍇	Gray{N0f8}🍇	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

❌ : to be fixed as a bug
🍇 : to be reconsidered in v0.10.0

[kimikage]

this PR

+	Bool	N0f8	Int64	Float32	Float64
Gray{Bool}	Gray{N0f8}🍇	Gray{N0f8}	Gray{N0f8}🍇	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float32}	Gray{Float64}
Gray24	Gray24	Gray24	Gray24🍇	Gray24🍇	Gray24🍇
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

+	Gray{Bool}	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Bool}	Gray{Bool}🆙	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

*	Bool	N0f8	Int64	Float32	Float64
Gray{Bool}	Gray{Bool}🆙	Gray{N0f8}	Gray{Float32}🆙	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}🍇	Gray{N0f8}🍇	Gray{Float32}	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

*	Gray{Bool}	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Bool}	Gray{Bool}🆙	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

/	Bool	N0f8	Int64	Float32	Float64
Gray{Bool}	Gray{Float32}🆙	Gray{N0f8}🍇	Gray{Float32}🆙	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}🍇	Gray{N0f8}	Gray{Float32}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}🍇	Gray{N0f8}🍇	Gray{Float32}	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

/	Gray{Bool}	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Bool}	Gray{Float32}🆙	Gray{N0f8}🍇	Gray{N0f8}🍇	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}🍇	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}🍇	Gray{N0f8}	Gray24	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

(Added) /	Gray{Bool}	Gray{N0f8}	Gray24	Gray{Float32}
Bool	Gray{Float32}🆙	Gray{N0f8}🍇	Gray24🍇	Gray{Float32}
N0f8	Gray{N0f8}🍇	Gray{N0f8}	Gray24	Gray{Float32}
Int64	Gray{Float32}🆙	Gray{Float32}	Gray24🍇	Gray{Float32}
Float32	Gray{Float32}	Gray{Float32}	Gray24🍇	Gray{Float32}
Float64	Gray{Float64}	Gray{Float64}	Gray24🍇	Gray{Float64}

(Added) ^	Bool	Int64	Float32	Float64
Gray{Bool}	Gray{Bool}🆙	Gray{Bool}🆙	Gray{Float32}	Gray{Float64}
Gray{N0f8}	Gray{N0f8}	Gray{N0f8}	Gray{Float32}	Gray{Float64}
Gray24	Gray{N0f8}🍇	Gray{N0f8}🍇	Gray{Float32}	Gray{Float64}
Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float32}	Gray{Float64}

🆙 : fixed in this PR
🍇 : to be reconsidered in v0.10.0

[johnnychen94]

Will this be more friendly to the compiler?

Suggested change

	divtype(::Type{Bool}, ::Type{B}) where {B} = divtype(B <: Integer ? N0f8 : UInt8, B)
	divtype(::Type{Bool}, ::Type{B}) where {B} = divtype(ifelse(B <: Integer, N0f8, UInt8), B)

[kimikage]

Do you have a specific example?
At least for me, the fewer parentheses, the friendlier it is. 😄

[johnnychen94]

No, but I think it's perfectly fine to evaluate both the true and false cases here as they're constant DataType.

From ?ifelse:
In some cases, using ifelse instead of an if statement can eliminate the branch in generated code and provide
higher performance in tight loops.

The @code_native looks the same for this case so I don't know if it worths. Maybe Julia is just smart enough to optimize it...

[kimikage]

Even using ifelse does not completely suppress the branches, so I simply prefer to keep it short and readable.
In the first place, since this is a matter of constant propagation (or dead code elimination), I don't think it has anything to do with the branch generation.

[kimikage]

I will merge this and release v0.9.5.
If you are lucky enough to find problems, I will fix them in v0.9.6. 😄