JuliaArrays / JuliaArrays/StaticArrays.jl

Unexpected Performance Difference between / and \

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linear-algebra performance
Dominant language
Julia
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Merged PRs (30d)
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Description

I noticed significant speed differences for left (\) and right(/) matrix division for 4 by 4 and bigger matrices. To my understanding, / is just mapped to \ and thus, I wouldn't expect these differences especially not / being faster than \. Does anyone know why this is happening?

julia> using StaticArrays, BenchmarkTools

julia> @benchmark a \ b setup = begin
                  a = rand(SMatrix{4, 4})
                  b = rand(SMatrix{4, 4})
              end
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     232.326 ns (0.00% GC)
  median time:      234.532 ns (0.00% GC)
  mean time:        260.624 ns (0.00% GC)
  maximum time:     1.799 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     442

julia> @benchmark a / b setup = begin
                  a = rand(SMatrix{4, 4})
                  b = rand(SMatrix{4, 4})
              end
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     183.468 ns (0.00% GC)
  median time:      184.085 ns (0.00% GC)
  mean time:        206.420 ns (0.00% GC)
  maximum time:     4.133 μs (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     681

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Research direction

Start with the benchmark examples in issue #585, comparing left () and right (/) division for StaticArrays SMatrix values of size 4×4 and larger. Reproduce both timings with Julia, StaticArrays, and BenchmarkTools, then inspect the division paths to determine why their performance differs. Done means the cause is identified and a focused fix or documented explanation is supported by benchmark results.

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Assessment

Tech stack
julia
Domain
performance
Issue type
Bug
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
35/100

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