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): 28.868 ns … 90.511 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 29.905 ns ┊ GC (median): 0.00%
Time (mean ± σ): 30.169 ns ± 1.709 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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28.9 ns Histogram: frequency by time 37.7 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 600 evaluations per sample.
Range (min … max): 198.788 ns … 426.982 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 200.743 ns ┊ GC (median): 0.00%
Time (mean ± σ): 203.144 ns ± 8.664 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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199 ns Histogram: frequency by time 226 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 v0.5.82-DEV `~/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): 378.394 ns … 600.335 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 384.714 ns ┊ GC (median): 0.00%
Time (mean ± σ): 388.220 ns ± 12.479 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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378 ns Histogram: log(frequency) by time 428 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): 4.686 μs … 11.407 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 4.723 μs ┊ GC (median): 0.00%
Time (mean ± σ): 4.785 μs ± 345.399 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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4.69 μs Histogram: log(frequency) by time 5.99 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): 6.676 μs … 16.425 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.707 μs ┊ GC (median): 0.00%
Time (mean ± σ): 6.778 μs ± 394.383 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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6.68 μs Histogram: log(frequency) by time 8.48 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 v0.5.82-DEV `~/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): 395.842 ns … 640.109 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 402.238 ns ┊ GC (median): 0.00%
Time (mean ± σ): 405.911 ns ± 13.522 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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396 ns Histogram: frequency by time 449 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
Di_SBP:
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.265 μs … 4.610 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.385 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.397 μs ± 109.469 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.27 μs Histogram: log(frequency) by time 2.12 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): 5.260 μs … 14.425 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 5.295 μs ┊ GC (median): 0.00%
Time (mean ± σ): 5.361 μs ± 388.696 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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5.26 μs Histogram: log(frequency) by time 6.67 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
Di_banded:
BenchmarkTools.Trial: 10000 samples with 5 evaluations per sample.
Range (min … max): 6.252 μs … 17.262 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.282 μs ┊ GC (median): 0.00%
Time (mean ± σ): 6.460 μs ± 467.177 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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6.25 μs Histogram: log(frequency) by time 8.36 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): 136.726 μs … 408.775 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 140.282 μs ┊ GC (median): 0.00%
Time (mean ± σ): 142.022 μs ± 5.737 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
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137 μs Histogram: frequency by time 158 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 v0.5.82-DEV `~/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, $u))Scalar case
D_SBP
BenchmarkTools.Trial: 10000 samples with 989 evaluations per sample.
Range (min … max): 46.629 ns … 77.313 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 47.288 ns ┊ GC (median): 0.00%
Time (mean ± σ): 47.748 ns ± 1.963 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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46.6 ns Histogram: log(frequency) by time 55.6 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 228 evaluations per sample.
Range (min … max): 326.048 ns … 701.882 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 333.741 ns ┊ GC (median): 0.00%
Time (mean ± σ): 337.645 ns ± 16.053 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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326 ns Histogram: frequency by time 380 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.712 μs … 5.300 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.725 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.746 μs ± 136.528 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.71 μs Histogram: log(frequency) by time 2.49 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we use a plain array of structures (AoS) in the form of a two-dimensional array and our custom mul_aos! implementation that loops over each component, using mul! on views. Here, the differences between the timings are less pronounced.
println("Plain Array of Structures")
u_aos_plain = randn(T, 5, size(D_SBP, 1)); du_aos_plain = similar(u_aos_plain)
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul_aos!($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, $u_aos_plain))Plain Array of Structures
D_SBP
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.304 μs … 3.619 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.312 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.324 μs ± 97.996 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.3 μs Histogram: log(frequency) by time 2.03 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 9 evaluations per sample.
Range (min … max): 2.367 μs … 7.618 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 2.436 μs ┊ GC (median): 0.00%
Time (mean ± σ): 2.461 μs ± 162.498 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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2.37 μs Histogram: log(frequency) by time 3.26 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 3 evaluations per sample.
Range (min … max): 8.750 μs … 20.328 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 8.816 μs ┊ GC (median): 0.00%
Time (mean ± σ): 8.958 μs ± 575.303 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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8.75 μs Histogram: log(frequency) by time 11.6 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Now, we use an array of structures (AoS) based on reinterpret and standard mul!. This is much more efficient for the implementation in SummationByPartsOperators.jl. In Julia v1.6, this is also more efficient for sparse matrices but less efficient for dense matrices (compared to the plain AoS approach with mul_aos! above).
println("Array of Structures (reinterpreted array)")
u_aos_r = reinterpret(reshape, Vec5{T}, u_aos_plain); du_aos_r = similar(u_aos_r)
@show D_SBP * u_aos_r ≈ D_sparse * u_aos_r ≈ D_full * u_aos_r
mul!(du_aos_r, D_SBP, u_aos_r)
@show reinterpret(reshape, T, du_aos_r) ≈ du_aos_plain
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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, $u_aos_r))Array of Structures (reinterpreted array)
D_SBP * u_aos_r ≈ D_sparse * u_aos_r ≈ D_full * u_aos_r = true
reinterpret(reshape, T, du_aos_r) ≈ du_aos_plain = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 525 evaluations per sample.
Range (min … max): 215.011 ns … 318.920 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 219.133 ns ┊ GC (median): 0.00%
Time (mean ± σ): 221.040 ns ± 6.064 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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215 ns Histogram: frequency by time 242 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 166 evaluations per sample.
Range (min … max): 636.976 ns … 934.699 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 665.886 ns ┊ GC (median): 0.00%
Time (mean ± σ): 670.983 ns ± 19.225 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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637 ns Histogram: frequency by time 729 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 4 evaluations per sample.
Range (min … max): 7.166 μs … 22.129 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.213 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.308 μs ± 593.720 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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7.17 μs Histogram: log(frequency) by time 9.2 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we still use an array of structures (AoS), but copy the data into a plain Array instead of using the reinterpreted versions. There is no significant difference to the previous version in this case.
println("Array of Structures")
u_aos = Array(u_aos_r); du_aos = similar(u_aos)
@show D_SBP * u_aos ≈ D_sparse * u_aos ≈ D_full * u_aos
mul!(du_aos, D_SBP, u_aos)
@show du_aos ≈ du_aos_r
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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, $u_aos))Array of Structures
D_SBP * u_aos ≈ D_sparse * u_aos ≈ D_full * u_aos = true
du_aos ≈ du_aos_r = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 550 evaluations per sample.
Range (min … max): 209.100 ns … 293.513 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 210.530 ns ┊ GC (median): 0.00%
Time (mean ± σ): 212.401 ns ± 5.532 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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209 ns Histogram: log(frequency) by time 231 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 184 evaluations per sample.
Range (min … max): 560.179 ns … 918.837 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 581.522 ns ┊ GC (median): 0.00%
Time (mean ± σ): 586.625 ns ± 18.311 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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560 ns Histogram: frequency by time 640 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 4 evaluations per sample.
Range (min … max): 7.248 μs … 22.545 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.436 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.515 μs ± 534.144 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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7.25 μs Histogram: log(frequency) by time 9.41 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Finally, let's look at a structure of arrays (SoA). Interestingly, this is slower than the array of structures we used above. On Julia v1.6, the sparse matrix representation performs particularly bad in this case.
println("Structure of Arrays")
u_soa = StructArray(u_aos); du_soa = similar(u_soa)
@show D_SBP * u_soa ≈ D_sparse * u_soa ≈ D_full * u_soa
mul!(du_soa, D_SBP, u_soa)
@show du_soa ≈ du_aos
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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 473 evaluations per sample.
Range (min … max): 225.241 ns … 314.023 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 227.677 ns ┊ GC (median): 0.00%
Time (mean ± σ): 229.662 ns ± 6.165 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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225 ns Histogram: frequency by time 250 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 213.921 μs … 5.646 ms ┊ GC (min … max): 0.00% … 93.16%
Time (median): 222.025 μs ┊ GC (median): 0.00%
Time (mean ± σ): 255.271 μs ± 366.968 μs ┊ GC (mean ± σ): 10.85% ± 7.18%
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214 μs Histogram: log(frequency) by time 364 μs <
Memory estimate: 328.25 KiB, allocs estimate: 10504.
D_full
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 174.366 μs … 5.508 ms ┊ GC (min … max): 0.00% … 95.64%
Time (median): 181.096 μs ┊ GC (median): 0.00%
Time (mean ± σ): 213.398 μs ± 371.280 μs ┊ GC (mean ± σ): 13.14% ± 7.25%
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174 μs Histogram: log(frequency) by time 321 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 v1.9.15
[09ab397b] StructArrays v0.6.18
[9f78cca6] SummationByPartsOperators v0.5.82-DEV `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl`