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 994 evaluations per sample.
Range (min … max): 30.107 ns … 61.141 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 31.245 ns ┊ GC (median): 0.00%
Time (mean ± σ): 31.572 ns ± 1.660 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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30.1 ns Histogram: log(frequency) by time 39.2 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 606 evaluations per sample.
Range (min … max): 198.739 ns … 428.589 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 200.789 ns ┊ GC (median): 0.00%
Time (mean ± σ): 202.937 ns ± 6.540 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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199 ns Histogram: frequency by time 218 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 v0.5.83 `~/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 204 evaluations per sample.
Range (min … max): 379.333 ns … 656.618 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 383.706 ns ┊ GC (median): 0.00%
Time (mean ± σ): 387.325 ns ± 13.323 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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379 ns Histogram: frequency by time 430 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): 4.534 μs … 12.121 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 4.568 μs ┊ GC (median): 0.00%
Time (mean ± σ): 4.625 μs ± 352.645 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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4.53 μs Histogram: log(frequency) by time 5.7 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): 6.701 μs … 16.755 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.734 μs ┊ GC (median): 0.00%
Time (mean ± σ): 6.805 μs ± 413.080 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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6.7 μs Histogram: log(frequency) by time 8.52 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 v0.5.83 `~/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): 381.650 ns … 780.768 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 386.384 ns ┊ GC (median): 0.00%
Time (mean ± σ): 390.011 ns ± 14.452 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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382 ns Histogram: frequency by time 431 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
Di_SBP:
BenchmarkTools.Trial: 10000 samples with 17 evaluations per sample.
Range (min … max): 973.588 ns … 2.689 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 980.059 ns ┊ GC (median): 0.00%
Time (mean ± σ): 991.480 ns ± 72.817 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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974 ns Histogram: log(frequency) by time 1.44 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): 5.186 μs … 12.313 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 5.342 μs ┊ GC (median): 0.00%
Time (mean ± σ): 5.407 μs ± 393.701 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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5.19 μs Histogram: log(frequency) by time 6.76 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
Di_banded:
BenchmarkTools.Trial: 10000 samples with 5 evaluations per sample.
Range (min … max): 6.213 μs … 13.485 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.242 μs ┊ GC (median): 0.00%
Time (mean ± σ): 6.412 μs ± 433.146 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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6.21 μs Histogram: log(frequency) by time 8.34 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): 148.067 μs … 387.324 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 150.271 μs ┊ GC (median): 0.00%
Time (mean ± σ): 152.437 μs ± 6.523 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
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148 μs Histogram: 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 v0.5.83 `~/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, $u))Scalar case
D_SBP
BenchmarkTools.Trial: 10000 samples with 988 evaluations per sample.
Range (min … max): 47.781 ns … 107.216 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 49.495 ns ┊ GC (median): 0.00%
Time (mean ± σ): 49.880 ns ± 2.150 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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47.8 ns Histogram: frequency by time 58 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 228 evaluations per sample.
Range (min … max): 324.601 ns … 684.127 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 330.750 ns ┊ GC (median): 0.00%
Time (mean ± σ): 334.308 ns ± 15.848 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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325 ns Histogram: frequency by time 371 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.715 μs … 5.151 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.724 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.745 μs ± 132.994 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.72 μs Histogram: log(frequency) by time 2.51 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we use a plain array of structures (AoS) in the form of a two-dimensional array and our custom mul_aos! implementation that loops over each component, using mul! on views. Here, the differences between the timings are less pronounced.
println("Plain Array of Structures")
u_aos_plain = randn(T, 5, size(D_SBP, 1)); du_aos_plain = similar(u_aos_plain)
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul_aos!($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, $u_aos_plain))Plain Array of Structures
D_SBP
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.298 μs … 3.438 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.312 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.326 μs ± 97.456 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.3 μs Histogram: log(frequency) by time 2.05 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 9 evaluations per sample.
Range (min … max): 2.366 μs … 6.029 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 2.426 μs ┊ GC (median): 0.00%
Time (mean ± σ): 2.452 μs ± 157.941 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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2.37 μs Histogram: log(frequency) by time 3.27 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 3 evaluations per sample.
Range (min … max): 8.937 μs … 25.047 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 8.987 μs ┊ GC (median): 0.00%
Time (mean ± σ): 9.108 μs ± 680.484 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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8.94 μs Histogram: log(frequency) by time 12 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Now, we use an array of structures (AoS) based on reinterpret and standard mul!. This is much more efficient for the implementation in SummationByPartsOperators.jl. In Julia v1.6, this is also more efficient for sparse matrices but less efficient for dense matrices (compared to the plain AoS approach with mul_aos! above).
println("Array of Structures (reinterpreted array)")
u_aos_r = reinterpret(reshape, Vec5{T}, u_aos_plain); du_aos_r = similar(u_aos_r)
@show D_SBP * u_aos_r ≈ D_sparse * u_aos_r ≈ D_full * u_aos_r
mul!(du_aos_r, D_SBP, u_aos_r)
@show reinterpret(reshape, T, du_aos_r) ≈ du_aos_plain
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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, $u_aos_r))Array of Structures (reinterpreted array)
D_SBP * u_aos_r ≈ D_sparse * u_aos_r ≈ D_full * u_aos_r = true
reinterpret(reshape, T, du_aos_r) ≈ du_aos_plain = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 555 evaluations per sample.
Range (min … max): 207.486 ns … 284.766 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 209.437 ns ┊ GC (median): 0.00%
Time (mean ± σ): 211.186 ns ± 4.927 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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207 ns Histogram: log(frequency) by time 226 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 186 evaluations per sample.
Range (min … max): 549.898 ns … 1.046 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 566.435 ns ┊ GC (median): 0.00%
Time (mean ± σ): 571.236 ns ± 17.448 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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550 ns Histogram: frequency by time 616 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 4 evaluations per sample.
Range (min … max): 7.096 μs … 18.677 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.158 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.264 μs ± 675.023 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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7.1 μs Histogram: log(frequency) by time 9.5 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we still use an array of structures (AoS), but copy the data into a plain Array instead of using the reinterpreted versions. There is no significant difference to the previous version in this case.
println("Array of Structures")
u_aos = Array(u_aos_r); du_aos = similar(u_aos)
@show D_SBP * u_aos ≈ D_sparse * u_aos ≈ D_full * u_aos
mul!(du_aos, D_SBP, u_aos)
@show du_aos ≈ du_aos_r
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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, $u_aos))Array of Structures
D_SBP * u_aos ≈ D_sparse * u_aos ≈ D_full * u_aos = true
du_aos ≈ du_aos_r = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 570 evaluations per sample.
Range (min … max): 204.979 ns … 381.539 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 207.668 ns ┊ GC (median): 0.00%
Time (mean ± σ): 209.422 ns ± 5.428 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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205 ns Histogram: frequency by time 224 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 189 evaluations per sample.
Range (min … max): 532.106 ns … 1.160 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 545.095 ns ┊ GC (median): 0.00%
Time (mean ± σ): 550.297 ns ± 20.351 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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532 ns Histogram: frequency by time 596 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 4 evaluations per sample.
Range (min … max): 7.281 μs … 21.285 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.349 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.441 μs ± 561.668 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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7.28 μs Histogram: log(frequency) by time 9.33 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Finally, let's look at a structure of arrays (SoA). Interestingly, this is slower than the array of structures we used above. On Julia v1.6, the sparse matrix representation performs particularly bad in this case.
println("Structure of Arrays")
u_soa = StructArray(u_aos); du_soa = similar(u_soa)
@show D_SBP * u_soa ≈ D_sparse * u_soa ≈ D_full * u_soa
mul!(du_soa, D_SBP, u_soa)
@show du_soa ≈ du_aos
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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 446 evaluations per sample.
Range (min … max): 230.769 ns … 364.022 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 234.070 ns ┊ GC (median): 0.00%
Time (mean ± σ): 235.943 ns ± 6.032 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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231 ns Histogram: frequency by time 255 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 214.311 μs … 5.806 ms ┊ GC (min … max): 0.00% … 95.47%
Time (median): 225.767 μs ┊ GC (median): 0.00%
Time (mean ± σ): 256.195 μs ± 361.926 μs ┊ GC (mean ± σ): 10.24% ± 6.91%
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214 μs Histogram: frequency by time 392 μs <
Memory estimate: 328.25 KiB, allocs estimate: 10504.
D_full
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 173.524 μs … 5.427 ms ┊ GC (min … max): 0.00% … 95.35%
Time (median): 181.078 μs ┊ GC (median): 0.00%
Time (mean ± σ): 208.796 μs ± 358.209 μs ┊ GC (mean ± σ): 12.46% ± 6.97%
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174 μs Histogram: frequency by time 312 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 v0.5.83 `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl`