Decouple size dictionary from EinExprs

[mofeing]

When manipulating EinExprs (e.g. creating, summing, ...), creation and merge of size dictionaries incurs into a large amount of allocations.

This PR decouples size dictionary from EinExpr and introduces SizedEinExpr: a EinExpr wrapper with a global index size dictionary.

julia> using EinExprs, BenchmarkTools

expr = sum([
    EinExpr([:j, :b, :i, :h], Dict(i => 2 for i in [:j, :b, :i, :h])),
    EinExpr([:a, :c, :e, :f], Dict(i => 2 for i in [:a, :c, :e, :f])),
    EinExpr([:j], Dict(i => 2 for i in [:j])),
    EinExpr([:e, :a, :g], Dict(i => 2 for i in [:e, :a, :g])),
    EinExpr([:f, :b], Dict(i => 2 for i in [:f, :b])),
    EinExpr([:i, :h, :d], Dict(i => 2 for i in [:i, :h, :d])),
    EinExpr([:d, :g, :c], Dict(i => 2 for i in [:d, :g, :c])),
])

@benchmark path = einexpr(Exhaustive(), expr)

Before

BenchmarkTools.Trial: 2442 samples with 1 evaluation.
 Range (min … max):  1.618 ms … 7.713 ms  ┊ GC (min … max):  0.00% … 42.34%
 Time  (median):     1.674 ms             ┊ GC (median):     0.00%
 Time  (mean ± σ):   2.046 ms ± 1.072 ms  ┊ GC (mean ± σ):  13.91% ± 16.30%

  █▆▂                                               ▁▁▁▁▁    
  ████▇▆▄▃▄▁▁▁▁▁▃▃▁▃▁▁▁▁▁▁▃▄▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▃▇██████▇ █
  1.62 ms     Histogram: log(frequency) by time     5.37 ms <

 Memory estimate: 4.51 MiB, allocs estimate: 65772.

After

BenchmarkTools.Trial: 9124 samples with 1 evaluation.
 Range (min … max):  400.167 μs …  14.535 ms  ┊ GC (min … max):  0.00% … 66.90%
 Time  (median):     425.625 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   546.911 μs ± 966.583 μs  ┊ GC (mean ± σ):  11.38% ±  6.06%

  █▂                                                            ▁
  ██▆▅▄▄▃▁▃▁▁▁▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▃▁▁▁▁▃▇▆ █
  400 μs        Histogram: log(frequency) by time       8.27 ms <

 Memory estimate: 621.73 KiB, allocs estimate: 11344.

[codecov]

Codecov Report

Attention: 20 lines in your changes are missing coverage. Please review.

Comparison is base (18f5783) 78.38% compared to head (47c64e5) 80.23%.
Report is 4 commits behind head on master.

Files	Patch %	Lines
src/SizedEinExpr.jl	77.50%	9 Missing ⚠️
src/Slicing.jl	56.25%	7 Missing ⚠️
src/Counters.jl	80.00%	2 Missing ⚠️
src/EinExpr.jl	95.23%	1 Missing ⚠️
src/Optimizers/Optimizers.jl	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #45      +/-   ##
==========================================
+ Coverage   78.38%   80.23%   +1.85%     
==========================================
  Files          11       12       +1     
  Lines         273      334      +61     
==========================================
+ Hits          214      268      +54     
- Misses         59       66       +7     

☔ View full report in Codecov by Sentry.
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[mofeing]

Greedy also exhibits a similar speedup and memory usage reduction.

Before

BenchmarkTools.Trial: 10000 samples with 7 evaluations.
 Range (min … max):  4.696 μs … 309.470 μs  ┊ GC (min … max): 0.00% … 96.32%
 Time  (median):     4.935 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   5.269 μs ±   9.726 μs  ┊ GC (mean ± σ):  6.01% ±  3.20%

                  ▁▃▄ ▆▇█▇ ▅▃▃                                 
  ▁▁▁▁▁▁▁▁▂▁▃▃▄▅▃▇███▇█████████▄▆▅▃▃▂▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▃
  4.7 μs          Histogram: frequency by time        5.33 μs <

 Memory estimate: 7.27 KiB, allocs estimate: 160.

After

BenchmarkTools.Trial: 10000 samples with 10 evaluations.
 Range (min … max):  1.913 μs … 252.412 μs  ┊ GC (min … max): 0.00% … 97.77%
 Time  (median):     1.988 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   2.117 μs ±   5.519 μs  ┊ GC (mean ± σ):  5.74% ±  2.18%

               ▁▂▄ ▅▇▇▇ █▇▆▅ ▄▃▂▂                              
  ▂▂▂▂▂▁▃▃▄▅▁▆████▁████▁████▁█████▁▇▆▅▅▁▄▄▃▃▁▃▂▂▂▂▁▂▂▂▂▁▂▂▂▂▂ ▄
  1.91 μs         Histogram: frequency by time        2.11 μs <

 Memory estimate: 2.39 KiB, allocs estimate: 43.