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): 28.837 ns … 55.189 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 29.401 ns ┊ GC (median): 0.00%
Time (mean ± σ): 29.703 ns ± 1.555 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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28.8 ns Histogram: log(frequency) by time 37.2 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): 200.224 ns … 540.793 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 204.146 ns ┊ GC (median): 0.00%
Time (mean ± σ): 207.208 ns ± 18.008 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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200 ns Histogram: frequency by time 235 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 v0.5.81 `~/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): 383.325 ns … 892.310 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 389.690 ns ┊ GC (median): 0.00%
Time (mean ± σ): 393.236 ns ± 13.731 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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383 ns Histogram: frequency by time 438 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): 4.806 μs … 10.085 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 4.846 μs ┊ GC (median): 0.00%
Time (mean ± σ): 4.897 μs ± 274.470 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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4.81 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): 6.753 μs … 16.182 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.797 μs ┊ GC (median): 0.00%
Time (mean ± σ): 6.878 μs ± 420.866 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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6.75 μs Histogram: log(frequency) by time 8.83 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 v0.5.81 `~/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 203 evaluations per sample.
Range (min … max): 381.404 ns … 596.931 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 386.729 ns ┊ GC (median): 0.00%
Time (mean ± σ): 390.139 ns ± 12.073 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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381 ns Histogram: frequency by time 431 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
Di_SBP:
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.023 μs … 2.511 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.032 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.042 μs ± 82.269 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.02 μs Histogram: frequency by time 1.74 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): 5.542 μs … 13.183 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 5.580 μs ┊ GC (median): 0.00%
Time (mean ± σ): 5.643 μs ± 350.225 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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5.54 μs Histogram: log(frequency) by time 6.89 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
Di_banded:
BenchmarkTools.Trial: 10000 samples with 5 evaluations per sample.
Range (min … max): 6.212 μs … 13.419 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.240 μs ┊ GC (median): 0.00%
Time (mean ± σ): 6.370 μs ± 414.100 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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6.21 μs Histogram: log(frequency) by time 8.25 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): 149.019 μs … 304.991 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 151.573 μs ┊ GC (median): 0.00%
Time (mean ± σ): 153.815 μs ± 5.700 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
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149 μs Histogram: log(frequency) by time 174 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 v0.5.81 `~/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, $u))Scalar case
D_SBP
BenchmarkTools.Trial: 10000 samples with 989 evaluations per sample.
Range (min … max): 46.011 ns … 73.574 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 46.639 ns ┊ GC (median): 0.00%
Time (mean ± σ): 47.133 ns ± 2.053 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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46 ns Histogram: frequency by time 56 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 221 evaluations per sample.
Range (min … max): 334.471 ns … 693.380 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 341.045 ns ┊ GC (median): 0.00%
Time (mean ± σ): 344.814 ns ± 14.335 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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334 ns Histogram: log(frequency) by time 387 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.711 μs … 4.068 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.727 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.746 μs ± 123.362 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.71 μs Histogram: log(frequency) by time 2.49 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we use a plain array of structures (AoS) in the form of a two-dimensional array and our custom mul_aos! implementation that loops over each component, using mul! on views. Here, the differences between the timings are less pronounced.
println("Plain Array of Structures")
u_aos_plain = randn(T, 5, size(D_SBP, 1)); du_aos_plain = similar(u_aos_plain)
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul_aos!($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, $u_aos_plain))Plain Array of Structures
D_SBP
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.302 μs … 3.571 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.310 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.326 μs ± 105.446 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.3 μs Histogram: log(frequency) by time 2.05 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 9 evaluations per sample.
Range (min … max): 2.595 μs … 6.139 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 2.735 μs ┊ GC (median): 0.00%
Time (mean ± σ): 2.761 μs ± 163.756 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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2.59 μs Histogram: frequency by time 3.58 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 3 evaluations per sample.
Range (min … max): 8.927 μs … 21.120 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 9.010 μs ┊ GC (median): 0.00%
Time (mean ± σ): 9.112 μs ± 556.238 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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8.93 μs Histogram: log(frequency) by time 11.6 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Now, we use an array of structures (AoS) based on reinterpret and standard mul!. This is much more efficient for the implementation in SummationByPartsOperators.jl. In Julia v1.6, this is also more efficient for sparse matrices but less efficient for dense matrices (compared to the plain AoS approach with mul_aos! above).
println("Array of Structures (reinterpreted array)")
u_aos_r = reinterpret(reshape, Vec5{T}, u_aos_plain); du_aos_r = similar(u_aos_r)
@show D_SBP * u_aos_r ≈ D_sparse * u_aos_r ≈ D_full * u_aos_r
mul!(du_aos_r, D_SBP, u_aos_r)
@show reinterpret(reshape, T, du_aos_r) ≈ du_aos_plain
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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, $u_aos_r))Array of Structures (reinterpreted array)
D_SBP * u_aos_r ≈ D_sparse * u_aos_r ≈ D_full * u_aos_r = true
reinterpret(reshape, T, du_aos_r) ≈ du_aos_plain = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 565 evaluations per sample.
Range (min … max): 205.039 ns … 293.257 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 207.955 ns ┊ GC (median): 0.00%
Time (mean ± σ): 209.792 ns ± 5.175 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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205 ns Histogram: frequency by time 226 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 162 evaluations per sample.
Range (min … max): 634.086 ns … 926.858 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 672.426 ns ┊ GC (median): 0.00%
Time (mean ± σ): 677.743 ns ± 19.151 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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634 ns Histogram: frequency by time 733 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 4 evaluations per sample.
Range (min … max): 7.073 μs … 18.107 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.144 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.237 μs ± 577.122 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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7.07 μs Histogram: log(frequency) by time 9.16 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we still use an array of structures (AoS), but copy the data into a plain Array instead of using the reinterpreted versions. There is no significant difference to the previous version in this case.
println("Array of Structures")
u_aos = Array(u_aos_r); du_aos = similar(u_aos)
@show D_SBP * u_aos ≈ D_sparse * u_aos ≈ D_full * u_aos
mul!(du_aos, D_SBP, u_aos)
@show du_aos ≈ du_aos_r
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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, $u_aos))Array of Structures
D_SBP * u_aos ≈ D_sparse * u_aos ≈ D_full * u_aos = true
du_aos ≈ du_aos_r = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 550 evaluations per sample.
Range (min … max): 209.027 ns … 282.418 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 210.922 ns ┊ GC (median): 0.00%
Time (mean ± σ): 212.814 ns ± 5.159 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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209 ns Histogram: log(frequency) by time 229 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 181 evaluations per sample.
Range (min … max): 583.961 ns … 946.304 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 595.033 ns ┊ GC (median): 0.00%
Time (mean ± σ): 600.433 ns ± 18.105 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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584 ns Histogram: frequency by time 653 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 4 evaluations per sample.
Range (min … max): 7.389 μs … 17.633 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.447 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.527 μs ± 435.778 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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7.39 μs Histogram: log(frequency) by time 9.52 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Finally, let's look at a structure of arrays (SoA). Interestingly, this is slower than the array of structures we used above. On Julia v1.6, the sparse matrix representation performs particularly bad in this case.
println("Structure of Arrays")
u_soa = StructArray(u_aos); du_soa = similar(u_soa)
@show D_SBP * u_soa ≈ D_sparse * u_soa ≈ D_full * u_soa
mul!(du_soa, D_SBP, u_soa)
@show du_soa ≈ du_aos
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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): 224.142 ns … 344.033 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 226.617 ns ┊ GC (median): 0.00%
Time (mean ± σ): 228.698 ns ± 6.908 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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224 ns Histogram: frequency by time 252 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 228.176 μs … 5.045 ms ┊ GC (min … max): 0.00% … 94.18%
Time (median): 234.608 μs ┊ GC (median): 0.00%
Time (mean ± σ): 266.069 μs ± 344.898 μs ┊ GC (mean ± σ): 9.89% ± 7.21%
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228 μs Histogram: log(frequency) by time 374 μs <
Memory estimate: 328.25 KiB, allocs estimate: 10504.
D_full
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 171.431 μs … 4.865 ms ┊ GC (min … max): 0.00% … 95.60%
Time (median): 175.979 μs ┊ GC (median): 0.00%
Time (mean ± σ): 206.767 μs ± 342.034 μs ┊ GC (mean ± σ): 12.64% ± 7.31%
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171 μs Histogram: log(frequency) by time 313 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 v0.5.81 `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl`