Refactor var/varm

[yuehhua]

Try to clarify the dependency between interfaces and implementations.
This also bring a little bit improvement in performance.

[yuehhua]

Test original benchmark in v1.3

julia> using Statistics

julia> using BenchmarkTools

julia> A = rand(10000);

julia> @benchmark var($A; mean=nothing)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     4.842 μs (0.00% GC)
  median time:      5.291 μs (0.00% GC)
  mean time:        5.727 μs (0.00% GC)
  maximum time:     19.203 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     7

julia> @benchmark var($A; mean=0.1)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     4.864 μs (0.00% GC)
  median time:      4.953 μs (0.00% GC)
  mean time:        5.280 μs (0.00% GC)
  maximum time:     12.545 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     7

julia> @benchmark varm($A, 0.1)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     2.670 μs (0.00% GC)
  median time:      2.878 μs (0.00% GC)
  mean time:        3.072 μs (0.00% GC)
  maximum time:     8.599 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     9

[yuehhua]

Benchmark after refactor

julia> using Statistics

julia> using BenchmarkTools

julia> A = rand(10000);

julia> @benchmark var($A; mean=nothing)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     4.881 μs (0.00% GC)
  median time:      4.908 μs (0.00% GC)
  mean time:        5.081 μs (0.00% GC)
  maximum time:     11.873 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     7

julia> @benchmark var($A; mean=0.1)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     4.882 μs (0.00% GC)
  median time:      4.910 μs (0.00% GC)
  mean time:        5.113 μs (0.00% GC)
  maximum time:     10.920 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     7

julia> @benchmark varm($A, 0.1)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     2.627 μs (0.00% GC)
  median time:      2.647 μs (0.00% GC)
  mean time:        2.763 μs (0.00% GC)
  maximum time:     7.039 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     9

[nalimilan]

Thanks. But do you have an idea of the behavior in terms of precision of the old and new algorithms when mean=nothing? Since there's virtually no performance improvement, we need strong reasons to move from one algorithm to the other. And why would we keep varm using one algorithm and var another one when mean !=nothing?

[mschauer]

Should we separate the question of which algorithm is called in the end from the general cleanup in this PR which is nice I believe?

[yuehhua]

Sorry for not following up this PR due to my busy time. This is still not much performance improvement but API improvement. Thanks for @mschauer's support. As for algorithm improvement, if I have time to address this issue, I will have another PR in the future.