Benchmarks
Here are some simple benchmarks. Take them with a grain of salt since they run on virtual machines in the cloud to generate the documentation automatically.
First-derivative operators
Periodic domains
Let's set up some benchmark code.
using BenchmarkTools
using LinearAlgebra, SparseArrays
using SummationByPartsOperators
BLAS.set_num_threads(1) # make sure that BLAS is serial to be fair
T = Float64
xmin, xmax = T(0), T(1)
D_SBP = periodic_derivative_operator(derivative_order=1, accuracy_order=2,
xmin=xmin, xmax=xmax, N=100)
x = grid(D_SBP)
D_sparse = sparse(D_SBP)
u = randn(eltype(D_SBP), length(x)); du = similar(u);
@show D_SBP * u ≈ D_sparse * u
function doit(D, text, du, u)
println(text)
sleep(0.1)
show(stdout, MIME"text/plain"(), @benchmark mul!($du, $D, $u))
println()
enddoit (generic function with 1 method)First, we benchmark the implementation from SummationByPartsOperators.jl.
doit(D_SBP, "D_SBP:", du, u)D_SBP:
BenchmarkTools.Trial: 10000 samples with 995 evaluations per sample.
Range (min … max): 28.405 ns … 56.013 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 29.079 ns ┊ GC (median): 0.00%
Time (mean ± σ): 29.740 ns ± 2.507 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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28.4 ns Histogram: log(frequency) by time 40.4 ns <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we compare this to the runtime obtained using a sparse matrix representation of the derivative operator. Depending on the hardware etc., this can be an order of magnitude slower than the optimized implementation from SummationByPartsOperators.jl.
doit(D_sparse, "D_sparse:", du, u)D_sparse:
BenchmarkTools.Trial: 10000 samples with 595 evaluations per sample.
Range (min … max): 199.664 ns … 530.279 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 202.576 ns ┊ GC (median): 0.00%
Time (mean ± σ): 206.141 ns ± 20.461 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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200 ns Histogram: frequency by time 237 ns <
Memory estimate: 0 bytes, allocs estimate: 0.These results were obtained using the following versions.
using InteractiveUtils
versioninfo()
using Pkg
Pkg.status(["SummationByPartsOperators"],
mode=PKGMODE_MANIFEST)Julia Version 1.6.7
Commit 3b76b25b64 (2022-07-19 15:11 UTC)
Platform Info:
OS: Linux (x86_64-pc-linux-gnu)
CPU: AMD EPYC 7763 64-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-11.0.1 (ORCJIT, generic)
Environment:
JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
Status `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl/docs/Manifest.toml`
[9f78cca6] SummationByPartsOperators v0.5.78 `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl`Bounded domains
We start again by setting up some benchmark code.
using BenchmarkTools
using LinearAlgebra, SparseArrays
using SummationByPartsOperators, BandedMatrices
BLAS.set_num_threads(1) # make sure that BLAS is serial to be fair
T = Float64
xmin, xmax = T(0), T(1)
D_SBP = derivative_operator(MattssonNordström2004(), derivative_order=1,
accuracy_order=6, xmin=xmin, xmax=xmax, N=10^3)
D_sparse = sparse(D_SBP)
D_banded = BandedMatrix(D_SBP)
u = randn(eltype(D_SBP), size(D_SBP, 1)); du = similar(u);
@show D_SBP * u ≈ D_sparse * u ≈ D_banded * u
function doit(D, text, du, u)
println(text)
sleep(0.1)
show(stdout, MIME"text/plain"(), @benchmark mul!($du, $D, $u))
println()
enddoit (generic function with 1 method)First, we benchmark the implementation from SummationByPartsOperators.jl.
doit(D_SBP, "D_SBP:", du, u)D_SBP:
BenchmarkTools.Trial: 10000 samples with 203 evaluations per sample.
Range (min … max): 388.458 ns … 949.892 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 392.448 ns ┊ GC (median): 0.00%
Time (mean ± σ): 397.167 ns ± 17.235 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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388 ns Histogram: log(frequency) by time 473 ns <
Memory estimate: 0 bytes, allocs estimate: 0.Again, we compare this to a representation of the derivative operator as a sparse matrix. No surprise - it is again much slower, as in periodic domains.
doit(D_sparse, "D_sparse:", du, u)D_sparse:
BenchmarkTools.Trial: 10000 samples with 7 evaluations per sample.
Range (min … max): 4.692 μs … 12.102 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 4.730 μs ┊ GC (median): 0.00%
Time (mean ± σ): 4.787 μs ± 328.958 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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4.69 μs Histogram: log(frequency) by time 5.93 μs <
Memory estimate: 0 bytes, allocs estimate: 0.FInally, we compare it to a representation as banded matrix. Disappointingly, this is still much slower than the optimized implementation from SummationByPartsOperators.jl.
doit(D_banded, "D_banded:", du, u)D_banded:
BenchmarkTools.Trial: 10000 samples with 5 evaluations per sample.
Range (min … max): 6.694 μs … 42.625 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.725 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.004 μs ± 1.400 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
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6.69 μs Histogram: log(frequency) by time 13 μs <
Memory estimate: 0 bytes, allocs estimate: 0.These results were obtained using the following versions.
using InteractiveUtils
versioninfo()
using Pkg
Pkg.status(["SummationByPartsOperators", "BandedMatrices"],
mode=PKGMODE_MANIFEST)Julia Version 1.6.7
Commit 3b76b25b64 (2022-07-19 15:11 UTC)
Platform Info:
OS: Linux (x86_64-pc-linux-gnu)
CPU: AMD EPYC 7763 64-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-11.0.1 (ORCJIT, generic)
Environment:
JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
Status `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl/docs/Manifest.toml`
[aae01518] BandedMatrices v1.7.6
[9f78cca6] SummationByPartsOperators v0.5.78 `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl`Dissipation operators
We follow the same structure as before. At first, we set up some benchmark code.
using BenchmarkTools
using LinearAlgebra, SparseArrays
using SummationByPartsOperators, BandedMatrices
BLAS.set_num_threads(1) # make sure that BLAS is serial to be fair
T = Float64
xmin, xmax = T(0), T(1)
D_SBP = derivative_operator(MattssonNordström2004(), derivative_order=1,
accuracy_order=6, xmin=xmin, xmax=xmax, N=10^3)
Di_SBP = dissipation_operator(MattssonSvärdNordström2004(), D_SBP)
Di_sparse = sparse(Di_SBP)
Di_banded = BandedMatrix(Di_SBP)
Di_full = Matrix(Di_SBP)
u = randn(eltype(D_SBP), size(D_SBP, 1)); du = similar(u);
@show Di_SBP * u ≈ Di_sparse * u ≈ Di_banded * u ≈ Di_full * u
function doit(D, text, du, u)
println(text)
sleep(0.1)
show(stdout, MIME"text/plain"(), @benchmark mul!($du, $D, $u))
println()
enddoit (generic function with 1 method)At first, let us benchmark the derivative and dissipation operators implemented in SummationByPartsOperators.jl.
doit(D_SBP, "D_SBP:", du, u)
doit(Di_SBP, "Di_SBP:", du, u)D_SBP:
BenchmarkTools.Trial: 10000 samples with 202 evaluations per sample.
Range (min … max): 388.094 ns … 699.366 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 392.213 ns ┊ GC (median): 0.00%
Time (mean ± σ): 396.380 ns ± 17.179 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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388 ns Histogram: frequency by time 441 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
Di_SBP:
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.013 μs … 2.709 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.021 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.032 μs ± 83.881 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.01 μs Histogram: frequency by time 1.73 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we compare the results to sparse matrix representations. It will not come as a surprise that these are again much (around an order of magnitude) slower.
doit(Di_sparse, "Di_sparse:", du, u)
doit(Di_banded, "Di_banded:", du, u)Di_sparse:
BenchmarkTools.Trial: 10000 samples with 6 evaluations per sample.
Range (min … max): 5.570 μs … 11.580 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 5.667 μs ┊ GC (median): 0.00%
Time (mean ± σ): 5.729 μs ± 323.804 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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5.57 μs Histogram: log(frequency) by time 7.02 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
Di_banded:
BenchmarkTools.Trial: 10000 samples with 5 evaluations per sample.
Range (min … max): 6.226 μs … 13.539 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.266 μs ┊ GC (median): 0.00%
Time (mean ± σ): 6.472 μs ± 471.714 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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6.23 μs Histogram: log(frequency) by time 8.33 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Finally, let's benchmark the same computation if a full (dense) matrix is used to represent the derivative operator. This is obviously a bad idea but 🤷
doit(Di_full, "Di_full:", du, u)Di_full:
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 150.039 μs … 327.548 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 155.654 μs ┊ GC (median): 0.00%
Time (mean ± σ): 156.847 μs ± 6.127 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
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150 μs Histogram: frequency by time 177 μs <
Memory estimate: 0 bytes, allocs estimate: 0.These results were obtained using the following versions.
using InteractiveUtils
versioninfo()
using Pkg
Pkg.status(["SummationByPartsOperators", "BandedMatrices"],
mode=PKGMODE_MANIFEST)Julia Version 1.6.7
Commit 3b76b25b64 (2022-07-19 15:11 UTC)
Platform Info:
OS: Linux (x86_64-pc-linux-gnu)
CPU: AMD EPYC 7763 64-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-11.0.1 (ORCJIT, generic)
Environment:
JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
Status `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl/docs/Manifest.toml`
[aae01518] BandedMatrices v1.7.6
[9f78cca6] SummationByPartsOperators v0.5.78 `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl`Structure-of-Arrays (SoA) and Array-of-Structures (AoS)
SummationByPartsOperators.jl tries to provide efficient support of
StaticVectors from StaticArrays.jl- StructArrays.jl
To demonstrate this, let us set up some benchmark code.
using BenchmarkTools
using StaticArrays, StructArrays
using LinearAlgebra, SparseArrays
using SummationByPartsOperators
BLAS.set_num_threads(1) # make sure that BLAS is serial to be fair
struct Vec5{T} <: FieldVector{5,T}
x1::T
x2::T
x3::T
x4::T
x5::T
end
# Apply `mul!` to each component of a plain array of structures one after another
function mul_aos!(du, D, u, args...)
for i in 1:size(du, 1)
mul!(view(du, i, :), D, view(u, i, :), args...)
end
end
T = Float64
xmin, xmax = T(0), T(1)
D_SBP = derivative_operator(MattssonNordström2004(), derivative_order=1,
accuracy_order=4, xmin=xmin, xmax=xmax, N=101)
D_sparse = sparse(D_SBP)
D_full = Matrix(D_SBP)101×101 Matrix{Float64}:
-141.176 173.529 -23.5294 … 0.0 0.0 0.0
-50.0 0.0 50.0 0.0 0.0 0.0
9.30233 -68.6047 0.0 0.0 0.0 0.0
3.06122 0.0 -60.2041 0.0 0.0 0.0
0.0 0.0 8.33333 0.0 0.0 0.0
0.0 0.0 0.0 … 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0
⋮ ⋱ ⋮
0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 … 0.0 0.0 0.0
0.0 0.0 0.0 -8.33333 0.0 0.0
0.0 0.0 0.0 60.2041 0.0 -3.06122
0.0 0.0 0.0 0.0 68.6047 -9.30233
0.0 0.0 0.0 -50.0 0.0 50.0
0.0 0.0 0.0 … 23.5294 -173.529 141.176At first, we benchmark the application of the operators implemented in SummationByPartsOperators.jl and their representations as sparse and dense matrices in the scalar case. As before, the sparse matrix representation is around an order of magnitude slower and the dense matrix representation is far off.
println("Scalar case")
u = randn(T, size(D_SBP, 1)); du = similar(u)
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($du, $D_SBP, $u))
println("\nD_sparse")
show(stdout, MIME"text/plain"(), @benchmark mul!($du, $D_sparse, $u))
println("\nD_full")
show(stdout, MIME"text/plain"(), @benchmark mul!($du, $D_full, $u))Scalar case
D_SBP
BenchmarkTools.Trial: 10000 samples with 989 evaluations per sample.
Range (min … max): 44.207 ns … 319.724 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 46.010 ns ┊ GC (median): 0.00%
Time (mean ± σ): 48.886 ns ± 13.814 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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44.2 ns Histogram: log(frequency) by time 102 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 221 evaluations per sample.
Range (min … max): 334.516 ns … 638.833 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 340.136 ns ┊ GC (median): 0.00%
Time (mean ± σ): 343.792 ns ± 13.825 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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335 ns Histogram: frequency by time 381 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.709 μs … 4.318 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.720 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.785 μs ± 229.894 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.71 μs Histogram: log(frequency) by time 2.72 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we use a plain array of structures (AoS) in the form of a two-dimensional array and our custom mul_aos! implementation that loops over each component, using mul! on views. Here, the differences between the timings are less pronounced.
println("Plain Array of Structures")
u_aos_plain = randn(T, 5, size(D_SBP, 1)); du_aos_plain = similar(u_aos_plain)
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul_aos!($du_aos_plain, $D_SBP, $u_aos_plain))
println("\nD_sparse")
show(stdout, MIME"text/plain"(), @benchmark mul_aos!($du_aos_plain, $D_sparse, $u_aos_plain))
println("\nD_full")
show(stdout, MIME"text/plain"(), @benchmark mul_aos!($du_aos_plain, $D_full, $u_aos_plain))Plain Array of Structures
D_SBP
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.310 μs … 2.922 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.321 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.337 μs ± 105.783 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.31 μs Histogram: log(frequency) by time 2.04 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 9 evaluations per sample.
Range (min … max): 2.353 μs … 4.921 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 2.403 μs ┊ GC (median): 0.00%
Time (mean ± σ): 2.427 μs ± 143.606 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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2.35 μs Histogram: log(frequency) by time 3.21 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 3 evaluations per sample.
Range (min … max): 8.970 μs … 17.562 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 9.020 μs ┊ GC (median): 0.00%
Time (mean ± σ): 9.110 μs ± 499.406 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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8.97 μs Histogram: log(frequency) by time 11.5 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Now, we use an array of structures (AoS) based on reinterpret and standard mul!. This is much more efficient for the implementation in SummationByPartsOperators.jl. In Julia v1.6, this is also more efficient for sparse matrices but less efficient for dense matrices (compared to the plain AoS approach with mul_aos! above).
println("Array of Structures (reinterpreted array)")
u_aos_r = reinterpret(reshape, Vec5{T}, u_aos_plain); du_aos_r = similar(u_aos_r)
@show D_SBP * u_aos_r ≈ D_sparse * u_aos_r ≈ D_full * u_aos_r
mul!(du_aos_r, D_SBP, u_aos_r)
@show reinterpret(reshape, T, du_aos_r) ≈ du_aos_plain
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($du_aos_r, $D_SBP, $u_aos_r))
println("\nD_sparse")
show(stdout, MIME"text/plain"(), @benchmark mul!($du_aos_r, $D_sparse, $u_aos_r))
println("\nD_full")
show(stdout, MIME"text/plain"(), @benchmark mul!($du_aos_r, $D_full, $u_aos_r))Array of Structures (reinterpreted array)
D_SBP * u_aos_r ≈ D_sparse * u_aos_r ≈ D_full * u_aos_r = true
reinterpret(reshape, T, du_aos_r) ≈ du_aos_plain = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 555 evaluations per sample.
Range (min … max): 207.845 ns … 366.932 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 211.474 ns ┊ GC (median): 0.00%
Time (mean ± σ): 213.503 ns ± 6.789 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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208 ns Histogram: log(frequency) by time 238 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 180 evaluations per sample.
Range (min … max): 585.361 ns … 1.062 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 594.544 ns ┊ GC (median): 0.00%
Time (mean ± σ): 600.845 ns ± 24.628 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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585 ns Histogram: frequency by time 677 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 4 evaluations per sample.
Range (min … max): 7.173 μs … 21.848 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.223 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.354 μs ± 825.307 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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7.17 μs Histogram: log(frequency) by time 11.1 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we still use an array of structures (AoS), but copy the data into a plain Array instead of using the reinterpreted versions. There is no significant difference to the previous version in this case.
println("Array of Structures")
u_aos = Array(u_aos_r); du_aos = similar(u_aos)
@show D_SBP * u_aos ≈ D_sparse * u_aos ≈ D_full * u_aos
mul!(du_aos, D_SBP, u_aos)
@show du_aos ≈ du_aos_r
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($du_aos, $D_SBP, $u_aos))
println("\nD_sparse")
show(stdout, MIME"text/plain"(), @benchmark mul!($du_aos, $D_sparse, $u_aos))
println("\nD_full")
show(stdout, MIME"text/plain"(), @benchmark mul!($du_aos, $D_full, $u_aos))Array of Structures
D_SBP * u_aos ≈ D_sparse * u_aos ≈ D_full * u_aos = true
du_aos ≈ du_aos_r = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 565 evaluations per sample.
Range (min … max): 205.673 ns … 991.308 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 208.742 ns ┊ GC (median): 0.00%
Time (mean ± σ): 211.187 ns ± 13.566 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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206 ns Histogram: log(frequency) by time 246 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 181 evaluations per sample.
Range (min … max): 582.735 ns … 2.579 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 592.260 ns ┊ GC (median): 0.00%
Time (mean ± σ): 600.023 ns ± 44.333 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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583 ns Histogram: frequency by time 673 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 4 evaluations per sample.
Range (min … max): 7.484 μs … 29.086 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.549 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.652 μs ± 687.726 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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7.48 μs Histogram: log(frequency) by time 9.56 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Finally, let's look at a structure of arrays (SoA). Interestingly, this is slower than the array of structures we used above. On Julia v1.6, the sparse matrix representation performs particularly bad in this case.
println("Structure of Arrays")
u_soa = StructArray(u_aos); du_soa = similar(u_soa)
@show D_SBP * u_soa ≈ D_sparse * u_soa ≈ D_full * u_soa
mul!(du_soa, D_SBP, u_soa)
@show du_soa ≈ du_aos
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($du_soa, $D_SBP, $u_soa))
println("\nD_sparse")
show(stdout, MIME"text/plain"(), @benchmark mul!($du_soa, $D_sparse, $u_soa))
println("\nD_full")
show(stdout, MIME"text/plain"(), @benchmark mul!($du_soa, $D_full, $u_soa))Structure of Arrays
D_SBP * u_soa ≈ D_sparse * u_soa ≈ D_full * u_soa = true
du_soa ≈ du_aos = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 478 evaluations per sample.
Range (min … max): 221.686 ns … 378.295 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 224.013 ns ┊ GC (median): 0.00%
Time (mean ± σ): 226.628 ns ± 9.738 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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222 ns Histogram: log(frequency) by time 287 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 211.873 μs … 6.382 ms ┊ GC (min … max): 0.00% … 62.02%
Time (median): 221.210 μs ┊ GC (median): 0.00%
Time (mean ± σ): 247.027 μs ± 299.088 μs ┊ GC (mean ± σ): 8.74% ± 6.87%
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212 μs Histogram: log(frequency) by time 363 μs <
Memory estimate: 328.25 KiB, allocs estimate: 10504.
D_full
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 177.028 μs … 4.542 ms ┊ GC (min … max): 0.00% … 93.62%
Time (median): 186.236 μs ┊ GC (median): 0.00%
Time (mean ± σ): 210.355 μs ± 291.538 μs ┊ GC (mean ± σ): 10.03% ± 6.90%
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177 μs Histogram: frequency by time 323 μs <
Memory estimate: 328.25 KiB, allocs estimate: 10504.These results were obtained using the following versions.
using InteractiveUtils
versioninfo()
using Pkg
Pkg.status(["SummationByPartsOperators", "StaticArrays", "StructArrays"],
mode=PKGMODE_MANIFEST)Julia Version 1.6.7
Commit 3b76b25b64 (2022-07-19 15:11 UTC)
Platform Info:
OS: Linux (x86_64-pc-linux-gnu)
CPU: AMD EPYC 7763 64-Core Processor
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-11.0.1 (ORCJIT, generic)
Environment:
JULIA_PKG_SERVER_REGISTRY_PREFERENCE = eager
Status `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl/docs/Manifest.toml`
[90137ffa] StaticArrays v1.9.13
[09ab397b] StructArrays v0.6.18
[9f78cca6] SummationByPartsOperators v0.5.78 `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl`