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improve performance of kernel(::SchoenbergQuarticSplineKernel, r, h) #253

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improve performance of kernel(::SchoenbergQuarticSplineKernel, r, h) #253

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d62972c
improve performance of kernel(::SchoenbergQuarticSplineKernel, r, h)
ranocha Oct 25, 2023
facba89
Update src/general/smoothing_kernels.jl
ranocha Oct 26, 2023
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2 changes: 2 additions & 0 deletions Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -9,6 +9,7 @@ DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def"
ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Morton = "2a6d852e-3fac-5a38-885c-fe708af2d09e"
MuladdMacro = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
Polyester = "f517fe37-dbe3-4b94-8317-1923a5111588"
Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
Expand All @@ -23,6 +24,7 @@ WriteVTK = "64499a7a-5c06-52f2-abe2-ccb03c286192"
DiffEqCallbacks = "2.25"
ForwardDiff = "0.10"
Morton = "0.1"
MuladdMacro = "0.2"
Polyester = "0.7.5"
Reexport = "1"
SciMLBase = "1, 2"
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1 change: 1 addition & 0 deletions src/TrixiParticles.jl
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Expand Up @@ -6,6 +6,7 @@ using Dates
using DiffEqCallbacks: PeriodicCallback, PeriodicCallbackAffect
using LinearAlgebra: norm, dot, I, tr
using Morton: cartesian2morton
using MuladdMacro: @muladd
using Polyester: Polyester, @batch
using Printf: @printf, @sprintf
using SciMLBase: CallbackSet, DiscreteCallback, DynamicalODEProblem, u_modified!,
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36 changes: 20 additions & 16 deletions src/general/smoothing_kernels.jl
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Expand Up @@ -163,24 +163,28 @@ For an analytic formula for higher order kernels, see (Monaghan, 1985).
"""
struct SchoenbergQuarticSplineKernel{NDIMS} <: SmoothingKernel{NDIMS} end

function kernel(kernel::SchoenbergQuarticSplineKernel, r::Real, h)
@muladd @inline function kernel(kernel::SchoenbergQuarticSplineKernel, r::Real, h)
q = r / h

if q >= 5 / 2
return 0.0
end

result = (5 / 2 - q)^4

if q < 3 / 2
result -= 5 * (3 / 2 - q)^4

if q < 1 / 2
result += 10 * (1 / 2 - q)^4
end
end

return normalization_factor(kernel, h) * result
# Note that `floating_point_number^integer_literal` is lowered to `Base.literal_pow`.
# Currently, specializations reducing this to simple multiplications exist only up
# to a power of three, see
# https://github.com/JuliaLang/julia/blob/34934736fa4dcb30697ac1b23d11d5ad394d6a4d/base/intfuncs.jl#L327-L339
# Higher powers just call a generic power implementation. Here, we accept to lose
# some precision but gain performance by using plain multiplications instead.
q5_2_pow4 = ((5 / 2 - q)^2)^2
q3_2_pow4 = ((3 / 2 - q)^2)^2
q1_2_pow4 = ((1 / 2 - q)^2)^2

# We do not use `+=` or `-=` since these are not recognized by MuladdMacro.jl.
result = q5_2_pow4
result = result - 5 * (q < 3 / 2) * q3_2_pow4
result = result + 10 * (q < 1 / 2) * q1_2_pow4

# Zero out result if q >= 5/2
result = ifelse(q < 5 / 2, normalization_factor(kernel, h) * result, zero(result))

return result
end

function kernel_deriv(kernel::SchoenbergQuarticSplineKernel, r::Real, h)
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