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slow performance #19

@brianguenter

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@brianguenter

Multiplying and adding UnitType numbers seems slow. Here's an example (not saying this is what you would necessarily do with unitful numbers but it has a lot of operations so it's easy to benchmark reliably):

julia> a =fill(u"m",(100,100))
100×100 Matrix{Meter}:

julia> b = rand(100,100);

julia> f(c) = c*c
f (generic function with 1 method)

julia> @benchmark f($a)
BenchmarkTools.Trial: 138 samples with 1 evaluation per sample.
 Range (min  max):  31.454 ms  53.650 ms  ┊ GC (min  max): 0.00%  0.00%
 Time  (median):     35.954 ms              ┊ GC (median):    6.07%
 Time  (mean ± σ):   36.352 ms ±  4.104 ms  ┊ GC (mean ± σ):  5.59% ± 4.95%

   █ ▆    ▁       ▂
  ██▆█▆▃▅▄█▄▄▅▄▄▆▇█▆▆▇▃▆▆▅▄▅▄▃▃▅▁▁▃▃▃▃▁▁▁▁▁▁▁▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▃ ▃
  31.5 ms         Histogram: frequency by time        53.2 ms <

 Memory estimate: 31.51 MiB, allocs estimate: 2050003.

julia> @benchmark f($b)
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
 Range (min  max):  23.300 μs    7.263 ms  ┊ GC (min  max): 0.00%  98.99%
 Time  (median):     29.400 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   38.380 μs ± 103.936 μs  ┊ GC (mean ± σ):  8.41% ±  4.47%

      ▄█▇▆▁
  ▂▁▂▄█████▅▄▃▂▂▂▂▂▂▂▁▁▁▁▁▁▁▂▄▅▆▆▅▅▄▄▅▄▃▃▃▃▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▂
  23.3 μs         Histogram: frequency by time         63.4 μs <

 Memory estimate: 78.20 KiB, allocs estimate: 3.

For this 100x100 matrix multiply the UnitType numbers take 1300 times longer than Float64 numbers and allocates 400 times as much.

When I run the same test using DynamicQuatitites.jl I get timing results that are identical to just using a Float64:

julia> @benchmark f($a)
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
 Range (min  max):  23.100 μs   11.849 ms  ┊ GC (min  max): 0.00%  99.47%
 Time  (median):     39.200 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   38.860 μs ± 147.260 μs  ┊ GC (mean ± σ):  8.90% ±  4.11%

   ▆█▃                              ▁
  ▂████▇▅▄▃▂▂▁▁▁▁▁▂▂▂▂▂▂▁▁▁▁▁▁▂▃▄▆████▇▆▅▄▃▃▃▂▂▂▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ▂
  23.1 μs         Histogram: frequency by time         58.2 μs <

 Memory estimate: 78.20 KiB, allocs estimate: 3.

julia> typeof(a)
QuantityArray(::Matrix{Float64}, ::Quantity{Float64, Dimensions{FixedRational{Int32, 25200}}})

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