Improve Lab<-->XYZ conversions

[kimikage]

This adds the separate methods for omitting the white points to facilitate constant folding.
This also suppresses the promotion of intermediate variables to Float64 due to white point being XYZ{Float64}. (cf. issue #477)

A part of this PR has been separated from PR #482.

I'm not sure of the reason, but I avoid mapc for now because it makes the precompilation problem worse. This PR does not solve the precompilation problem. 😕

[kimikage]

Benchmark

using Colors, BenchmarkTools
rgb_f64 = rand(RGB{Float64}, 1000, 1000);
xyz_f64 = XYZ{Float64}.(rgb_f64);
xyz_f32 = XYZ{Float32}.(xyz_f64);
lab_f64 = Lab{Float64}.(xyz_f64);
lab_f32 = Lab{Float32}.(lab_f64);

function Colors.fxyz2lab(v) # force invalidation
    ka = oftype(v, 841 / 108) # (29/6)^2 / 3 = xyz_kappa / 116
    kb = oftype(v, 16 / 116) # 4/29
    v > oftype(v, Colors.xyz_epsilon) ? cbrt(v) : muladd(ka, v, kb)
end

julia> @btime convert.(XYZ, $lab_f64);
  7.433 ms (2 allocations: 22.89 MiB) # before
  5.433 ms (2 allocations: 22.89 MiB) # after

julia> @btime convert.(XYZ, $lab_f32);
  11.288 ms (2 allocations: 11.44 MiB) # before
  2.359 ms (2 allocations: 11.44 MiB) # after

julia> @btime convert.(Lab, $xyz_f64);
  31.515 ms (2 allocations: 22.89 MiB) # before
  29.489 ms (2 allocations: 22.89 MiB) # after

julia> @btime convert.(Lab, $xyz_f32);
  33.801 ms (2 allocations: 11.44 MiB) # before
  23.568 ms (2 allocations: 11.44 MiB) # after

[codecov]

Codecov Report

Merging #486 (34d8a0c) into master (4645452) will increase coverage by 0.29%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #486      +/-   ##
==========================================
+ Coverage   92.82%   93.12%   +0.29%     
==========================================
  Files           9        9              
  Lines        1004     1018      +14     
==========================================
+ Hits          932      948      +16     
+ Misses         72       70       -2     

Impacted Files	Coverage Δ
src/conversions.jl	99.68% <100.00%> (+0.67%)	⬆️

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[johnnychen94]

I'm not sure of the reason, but I avoid mapc for now because it makes the precompilation problem worse.

Are there any related issues to this?

Edit:

Oh, I guess you mean you're doing a manual inline? 😄

[kimikage]

Oh, I guess you mean you're doing a manual inline? 😄

Right. That's exactly what you presumed.
The mapc for white point scaling was manually inlined just for the purpose of constant folding. On the other hand, mapc(fxyz2lab, c) is causing invalidation to not work properly. 😵

[kimikage]

As mentioned in #427 (comment), this avoidance of divisions is effective on the Lab-->XYZ conversion.

The accuracy is mostly equivalent to the division version, in the environment that supports the FMA instruction.

[kimikage]

Note that the constant folding of WP_DEFAULT is also effective for Luv. I plan to submit a separate PR after merging the PR #489. I am still tweaking the cube root for Float32.