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3 argument dot is slower than a matmul and two arg dot #1287
Description
Somewhat counter intuitive:
using LinearAlgebra, StaticArrays, BenchmarkTools
f1(x, A) = dot(x, A * x)
f2(x, A) = dot(x, A, x)
let
x = randn(3)
A = randn(3, 3)
A = A * A' + 1e-6 * I
sx = SVector{3}(x...)
sA = SMatrix{3,3}(A...)
display(@benchmark(f1($sx, $sA)))
display(@benchmark(f2($sx, $sA)))
end
BenchmarkTools.Trial: 10000 samples with 1000 evaluations.
Range (min … max): 2.813 ns … 18.835 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 2.817 ns ┊ GC (median): 0.00%
Time (mean ± σ): 2.878 ns ± 0.673 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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2.81 ns Histogram: log(frequency) by time 3.54 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
BenchmarkTools.Trial: 10000 samples with 1000 evaluations.
Range (min … max): 3.815 ns … 54.783 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 3.821 ns ┊ GC (median): 0.00%
Time (mean ± σ): 3.931 ns ± 1.141 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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3.82 ns Histogram: log(frequency) by time 5.3 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
julia> versioninfo()
Julia Version 1.11.1
Commit 8f5b7ca12ad (2024-10-16 10:53 UTC)
Build Info:
Official https://julialang.org/ release
Platform Info:
OS: Linux (x86_64-linux-gnu)
CPU: 16 × 11th Gen Intel(R) Core(TM) i7-11700K @ 3.60GHz
WORD_SIZE: 64
LLVM: libLLVM-16.0.6 (ORCJIT, rocketlake)
Threads: 16 default, 0 interactive, 8 GC (on 16 virtual cores)
Environment:
JULIA_EDITOR = code
JULIA_NUM_THREADS = 16
Activity
kbarros commentedon Oct 26, 2026
I hit this also. A simple fix would be the method overload:
Would this be welcomed as a PR?
kbarros commentedon Oct 29, 2026
Also, apparently
u' * A * vtranslates todot(u, A, v), so this is not an esoteric situation.