Accelerate recursive Mul

[putianyi889]

This change only takes effect after JuliaArrays/LazyArrays.jl#261

using LazyArrays

A = ApplyArray(*, [ones(10,10) for _ in 1:10]...);
@time for m in 1:10, n in 1:10
    A[m,n]
end

B = ones(10,10)
for k in 1:5
    B = ApplyArray(*, B, B)
end
@time for m in 1:10, n in 1:10
    B[m,n]
end

C = ones(10,10)
M = Mul(C, C)
@time for m in 1:10, n in 1:10
    M[m,n]
end

Before: exponential in depth

256.268356 seconds (451.16 M allocations: 13.413 GiB, 1.39% gc time)
0.615169 seconds (3.37 M allocations: 105.647 MiB, 4.57% gc time)
0.000029 seconds (100 allocations: 1.562 KiB)

After: linear in operations

0.003850 seconds (4.50 k allocations: 1.401 MiB)
0.059771 seconds (27.50 k allocations: 6.798 MiB)
0.000078 seconds (300 allocations: 29.688 KiB)

[codecov]

Codecov Report

Patch coverage: 100.00% and project coverage change: +0.02% 🎉

Comparison is base (a7786a0) 86.49% compared to head (e893bea) 86.51%.
Report is 7 commits behind head on master.

❗ Current head e893bea differs from pull request most recent head dbeb413. Consider uploading reports for the commit dbeb413 to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #153      +/-   ##
==========================================
+ Coverage   86.49%   86.51%   +0.02%     
==========================================
  Files          10       10              
  Lines        1740     1765      +25     
==========================================
+ Hits         1505     1527      +22     
- Misses        235      238       +3     

Files Changed	Coverage Δ
src/ArrayLayouts.jl	79.58% <100.00%> (-2.55%)	⬇️
src/memorylayout.jl	84.53% <100.00%> (+0.34%)	⬆️
src/mul.jl	84.50% <100.00%> (+2.60%)	⬆️

... and 1 file with indirect coverage changes

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[putianyi889]

solves JuliaArrays/LazyArrays.jl#259

[dlfivefifty]

As we discussed, I think this should be in lazy arrays and only when of the layouts are ApplyLayout{typeof(*)}. Otherwise the old version is allocation free.

[dlfivefifty]

I've reopened as your proposal on maybeview might be a better approach. Though we'd have to make sure it works

[putianyi889]

Though we'd have to make sure it works

I'm using a custom lazyview on my other branch and it's working fine. Overwriting maybeview is type piracy and needs more consideration.

[dlfivefifty]

Maybe call it something descriptive like this:

"""
fast_maybeview(A, kr...)

returns a view if indexing is fast, otherwise calls `A[kr...]` to efficiently materialise an array.
""""
fast_maybeview(A, kr...) = ...

[putianyi889]

or just fastview?

Edit: it doesn't work like view since setindex! doesn't always work. I prefer maybeview_layout as it's consistent with other naming conventions

[dlfivefifty]

I think JuliaArrays/LazyArrays.jl#268 makes this unnecessary