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): 29.573 ns … 78.589 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 30.540 ns ┊ GC (median): 0.00%
Time (mean ± σ): 30.788 ns ± 1.564 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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29.6 ns Histogram: frequency by time 37.9 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 232 evaluations per sample.
Range (min … max): 311.401 ns … 687.233 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 336.103 ns ┊ GC (median): 0.00%
Time (mean ± σ): 339.156 ns ± 12.020 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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311 ns Histogram: frequency by time 375 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 v0.5.84 `~/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): 379.926 ns … 657.064 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 384.784 ns ┊ GC (median): 0.00%
Time (mean ± σ): 388.166 ns ± 12.407 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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380 ns Histogram: frequency by time 431 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): 4.902 μs … 10.945 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 4.946 μs ┊ GC (median): 0.00%
Time (mean ± σ): 4.997 μs ± 285.020 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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4.9 μs Histogram: log(frequency) by time 6.03 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): 6.677 μs … 15.092 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.700 μs ┊ GC (median): 0.00%
Time (mean ± σ): 6.784 μs ± 439.685 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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6.68 μs Histogram: log(frequency) by time 8.67 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 v0.5.84 `~/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): 382.537 ns … 595.300 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 387.719 ns ┊ GC (median): 0.00%
Time (mean ± σ): 390.977 ns ± 11.784 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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383 ns Histogram: frequency by time 430 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
Di_SBP:
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.011 μs … 2.824 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.020 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.030 μs ± 82.510 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.01 μs Histogram: log(frequency) by time 1.72 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): 5.243 μs … 13.519 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 5.275 μs ┊ GC (median): 0.00%
Time (mean ± σ): 5.333 μs ± 326.007 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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5.24 μs Histogram: log(frequency) by time 6.57 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
Di_banded:
BenchmarkTools.Trial: 10000 samples with 5 evaluations per sample.
Range (min … max): 6.224 μs … 15.727 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 6.264 μs ┊ GC (median): 0.00%
Time (mean ± σ): 6.459 μs ± 503.034 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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6.22 μs Histogram: log(frequency) by time 8.37 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): 133.639 μs … 314.598 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 135.042 μs ┊ GC (median): 0.00%
Time (mean ± σ): 137.203 μs ± 6.030 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
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134 μs Histogram: log(frequency) by time 159 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 v0.5.84 `~/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, $u))Scalar case
D_SBP
BenchmarkTools.Trial: 10000 samples with 989 evaluations per sample.
Range (min … max): 46.092 ns … 74.679 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 46.690 ns ┊ GC (median): 0.00%
Time (mean ± σ): 47.163 ns ± 1.929 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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46.1 ns Histogram: log(frequency) by time 54.9 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 222 evaluations per sample.
Range (min … max): 334.450 ns … 613.356 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 340.590 ns ┊ GC (median): 0.00%
Time (mean ± σ): 344.322 ns ± 13.599 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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334 ns Histogram: frequency by time 384 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.718 μs … 4.502 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.732 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.756 μs ± 137.742 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.72 μs Histogram: log(frequency) by time 2.49 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we use a plain array of structures (AoS) in the form of a two-dimensional array and our custom mul_aos! implementation that loops over each component, using mul! on views. Here, the differences between the timings are less pronounced.
println("Plain Array of Structures")
u_aos_plain = randn(T, 5, size(D_SBP, 1)); du_aos_plain = similar(u_aos_plain)
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul_aos!($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, $u_aos_plain))Plain Array of Structures
D_SBP
BenchmarkTools.Trial: 10000 samples with 10 evaluations per sample.
Range (min … max): 1.296 μs … 3.824 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 1.308 μs ┊ GC (median): 0.00%
Time (mean ± σ): 1.321 μs ± 100.167 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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1.3 μs Histogram: log(frequency) by time 2.02 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 9 evaluations per sample.
Range (min … max): 2.582 μs … 5.993 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 2.815 μs ┊ GC (median): 0.00%
Time (mean ± σ): 2.845 μs ± 174.083 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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2.58 μs Histogram: frequency by time 3.66 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 3 evaluations per sample.
Range (min … max): 8.753 μs … 18.448 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 8.800 μs ┊ GC (median): 0.00%
Time (mean ± σ): 8.897 μs ± 536.245 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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8.75 μs Histogram: log(frequency) by time 11.4 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Now, we use an array of structures (AoS) based on reinterpret and standard mul!. This is much more efficient for the implementation in SummationByPartsOperators.jl. In Julia v1.6, this is also more efficient for sparse matrices but less efficient for dense matrices (compared to the plain AoS approach with mul_aos! above).
println("Array of Structures (reinterpreted array)")
u_aos_r = reinterpret(reshape, Vec5{T}, u_aos_plain); du_aos_r = similar(u_aos_r)
@show D_SBP * u_aos_r ≈ D_sparse * u_aos_r ≈ D_full * u_aos_r
mul!(du_aos_r, D_SBP, u_aos_r)
@show reinterpret(reshape, T, du_aos_r) ≈ du_aos_plain
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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, $u_aos_r))Array of Structures (reinterpreted array)
D_SBP * u_aos_r ≈ D_sparse * u_aos_r ≈ D_full * u_aos_r = true
reinterpret(reshape, T, du_aos_r) ≈ du_aos_plain = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 550 evaluations per sample.
Range (min … max): 207.896 ns … 303.258 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 210.485 ns ┊ GC (median): 0.00%
Time (mean ± σ): 212.259 ns ± 5.208 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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208 ns Histogram: frequency by time 229 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 29 evaluations per sample.
Range (min … max): 907.552 ns … 2.070 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 965.276 ns ┊ GC (median): 0.00%
Time (mean ± σ): 974.051 ns ± 51.994 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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908 ns Histogram: log(frequency) by time 1.22 μs <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 4 evaluations per sample.
Range (min … max): 7.356 μs … 21.139 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.419 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.514 μs ± 601.684 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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7.36 μs Histogram: log(frequency) by time 9.52 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Next, we still use an array of structures (AoS), but copy the data into a plain Array instead of using the reinterpreted versions. There is no significant difference to the previous version in this case.
println("Array of Structures")
u_aos = Array(u_aos_r); du_aos = similar(u_aos)
@show D_SBP * u_aos ≈ D_sparse * u_aos ≈ D_full * u_aos
mul!(du_aos, D_SBP, u_aos)
@show du_aos ≈ du_aos_r
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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, $u_aos))Array of Structures
D_SBP * u_aos ≈ D_sparse * u_aos ≈ D_full * u_aos = true
du_aos ≈ du_aos_r = true
D_SBP
BenchmarkTools.Trial: 10000 samples with 555 evaluations per sample.
Range (min … max): 206.944 ns … 279.259 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 209.670 ns ┊ GC (median): 0.00%
Time (mean ± σ): 211.392 ns ± 4.982 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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207 ns Histogram: frequency by time 228 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 176 evaluations per sample.
Range (min … max): 601.807 ns … 1.122 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 621.330 ns ┊ GC (median): 0.00%
Time (mean ± σ): 636.268 ns ± 56.908 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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602 ns Histogram: log(frequency) by time 928 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_full
BenchmarkTools.Trial: 10000 samples with 4 evaluations per sample.
Range (min … max): 7.376 μs … 17.813 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 7.429 μs ┊ GC (median): 0.00%
Time (mean ± σ): 7.504 μs ± 439.049 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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7.38 μs Histogram: log(frequency) by time 9.34 μs <
Memory estimate: 0 bytes, allocs estimate: 0.Finally, let's look at a structure of arrays (SoA). Interestingly, this is slower than the array of structures we used above. On Julia v1.6, the sparse matrix representation performs particularly bad in this case.
println("Structure of Arrays")
u_soa = StructArray(u_aos); du_soa = similar(u_soa)
@show D_SBP * u_soa ≈ D_sparse * u_soa ≈ D_full * u_soa
mul!(du_soa, D_SBP, u_soa)
@show du_soa ≈ du_aos
println("D_SBP")
show(stdout, MIME"text/plain"(), @benchmark mul!($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 460 evaluations per sample.
Range (min … max): 235.026 ns … 355.533 ns ┊ GC (min … max): 0.00% … 0.00%
Time (median): 237.465 ns ┊ GC (median): 0.00%
Time (mean ± σ): 239.446 ns ± 6.391 ns ┊ GC (mean ± σ): 0.00% ± 0.00%
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235 ns Histogram: frequency by time 259 ns <
Memory estimate: 0 bytes, allocs estimate: 0.
D_sparse
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 211.957 μs … 6.624 ms ┊ GC (min … max): 0.00% … 95.95%
Time (median): 220.853 μs ┊ GC (median): 0.00%
Time (mean ± σ): 256.440 μs ± 425.821 μs ┊ GC (mean ± σ): 12.04% ± 6.96%
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212 μs Histogram: log(frequency) by time 387 μs <
Memory estimate: 328.25 KiB, allocs estimate: 10504.
D_full
BenchmarkTools.Trial: 10000 samples with 1 evaluation per sample.
Range (min … max): 178.764 μs … 6.403 ms ┊ GC (min … max): 0.00% … 96.61%
Time (median): 184.780 μs ┊ GC (median): 0.00%
Time (mean ± σ): 220.373 μs ± 435.571 μs ┊ GC (mean ± σ): 14.33% ± 7.00%
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179 μs Histogram: log(frequency) by time 318 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 v0.5.84 `~/work/SummationByPartsOperators.jl/SummationByPartsOperators.jl`