precompile.jl

#=
The code contained in this file is inspired by an analysis performed
using SnoopCompile, although most of it is written manually.

This kind of analysis was performed using the following code.
```julia
using SnoopCompile
inf_timing = @snoopi tmin=0.01 begin
  # below is mostly a copy of `examples/2d/elixir_advection_amr.jl`
  using Trixi
  using OrdinaryDiffEq

  ###############################################################################
  # semidiscretization of the linear advection equation

  advection_velocity = (1.0, 1.0)
  equations = LinearScalarAdvectionEquation2D(advection_velocity)
  show(stdout, equations)
  show(stdout, MIME"text/plain"(), equations)

  initial_condition = initial_condition_gauss

  surface_flux = flux_lax_friedrichs
  basis = LobattoLegendreBasis(3)
  solver = DGSEM(basis, surface_flux)
  show(stdout, solver)
  show(stdout, MIME"text/plain"(), solver)

  coordinates_min = (-5, -5)
  coordinates_max = ( 5,  5)
  mesh = TreeMesh(coordinates_min, coordinates_max,
                  initial_refinement_level=4,
                  n_cells_max=30_000)
  show(stdout, mesh)
  show(stdout, MIME"text/plain"(), mesh)

  semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver)
  show(stdout, semi)
  show(stdout, MIME"text/plain"(), semi)

  ###############################################################################
  # ODE solvers, callbacks etc.

  tspan = (0.0, 10.0)
  ode = semidiscretize(semi, tspan)

  summary_callback = SummaryCallback()
  show(stdout, summary_callback)
  show(stdout, MIME"text/plain"(), summary_callback)

  amr_controller = ControllerThreeLevel(semi, IndicatorMax(semi, variable=first),
                                        base_level=4,
                                        med_level=5, med_threshold=0.1,
                                        max_level=6, max_threshold=0.6)
  amr_callback = AMRCallback(semi, amr_controller,
                            interval=5,
                            adapt_initial_condition=true,
                            adapt_initial_condition_only_refine=true)
  show(stdout, amr_callback)
  show(stdout, MIME"text/plain"(), amr_callback)

  stepsize_callback = StepsizeCallback(cfl=1.6)
  show(stdout, stepsize_callback)
  show(stdout, MIME"text/plain"(), stepsize_callback)

  save_solution = SaveSolutionCallback(interval=100,
                                      save_initial_solution=true,
                                      save_final_solution=true,
                                      solution_variables=cons2prim)
  show(stdout, save_solution)
  show(stdout, MIME"text/plain"(), save_solution)

  save_restart = SaveRestartCallback(interval=100,
                                    save_final_restart=true)
  show(stdout, save_restart)
  show(stdout, MIME"text/plain"(), save_restart)

  analysis_interval = 100
  alive_callback = AliveCallback(analysis_interval=analysis_interval)
  show(stdout, alive_callback)
  show(stdout, MIME"text/plain"(), alive_callback)
  analysis_callback = AnalysisCallback(equations, solver,
                                      interval=analysis_interval,
                                      extra_analysis_integrals=(entropy,))
  show(stdout, analysis_callback)
  show(stdout, MIME"text/plain"(), analysis_callback)

  callbacks = CallbackSet(summary_callback,
                          save_restart, save_solution,
                          analysis_callback, alive_callback,
                          amr_callback, stepsize_callback);

  ###############################################################################
  # run the simulation

  u_ode = copy(ode.u0)
  du_ode = similar(u_ode)
  Trixi.rhs!(du_ode, u_ode, semi, first(tspan))

  # You could also include a `solve` stage to generate possibly more precompile statements.
  # sol = Trixi.solve(ode, Trixi.SimpleAlgorithm2N45(),
  #                   dt=stepsize_callback(ode), # solve needs some value here but it will be overwritten by the stepsize_callback
  #                   save_everystep=false, callback=callbacks);
  summary_callback() # print the timer summary
end
pc = SnoopCompile.parcel(inf_timing)
SnoopCompile.write("dev/precompile", pc)

```
After running the code above, SnoopCompile has generated the file
`dev/precompile/precompile_Trixi.jl`, which contains precompile statements
in the function `_precompile_`.
More information on this process can be found in the docs of SnoopCompile,
in particular at https://timholy.github.io/SnoopCompile.jl/stable/snoopi/.

This kind of analysis helps finding type-unstable parts of the code, e.g.
`init_interfaces` etc. in https://github.com/trixi-framework/Trixi.jl/pull/307.
Moreover, it allows to generate precompile statements which reduce the latency
by caching type inference results.
The latency can be measured by running
```bash
julia --threads=1 -e '@time using Trixi; @time include(joinpath(examples_dir(), "2d", "elixir_advection_basic.jl"))'
```

We add `@assert` to the precompile statements below to make sure that we don't include
failing precompile statements, cf. https://timholy.github.io/SnoopCompile.jl/stable/snoopi/.
If any assertions below fail, it is generally safe to just disable the failing call
to precompile (or to not include precompile.jl at all).
To still get the same latency reductions, you should consider to adapt the failing precompile
statements in accordance with the changes in Trixi.jl's source code. Please, feel free to ping
the core developers of Trixi.jl to get help with that.
=#

import StaticArrays
import SciMLBase

# manually generated precompile statements
function _precompile_manual_()
    ccall(:jl_generating_output, Cint, ()) == 1 || return nothing

    function equations_types_1d(RealT)
        (LinearScalarAdvectionEquation1D{RealT},
         HyperbolicDiffusionEquations1D{RealT},
         CompressibleEulerEquations1D{RealT},
         IdealGlmMhdEquations1D{RealT})
    end
    function equations_types_2d(RealT)
        (LinearScalarAdvectionEquation2D{RealT},
         HyperbolicDiffusionEquations2D{RealT},
         CompressibleEulerEquations2D{RealT},
         IdealGlmMhdEquations2D{RealT},
         LatticeBoltzmannEquations2D{RealT, typeof(Trixi.collision_bgk)})
    end
    function equations_types_3d(RealT)
        (LinearScalarAdvectionEquation3D{RealT},
         HyperbolicDiffusionEquations3D{RealT},
         CompressibleEulerEquations3D{RealT},
         IdealGlmMhdEquations3D{RealT},
         LatticeBoltzmannEquations3D{RealT, typeof(Trixi.collision_bgk)})
    end
    function equations_types(RealT)
        (LinearScalarAdvectionEquation1D{RealT},
         LinearScalarAdvectionEquation2D{RealT},
         LinearScalarAdvectionEquation3D{RealT},
         HyperbolicDiffusionEquations1D{RealT},
         HyperbolicDiffusionEquations2D{RealT},
         HyperbolicDiffusionEquations3D{RealT},
         CompressibleEulerEquations1D{RealT},
         CompressibleEulerEquations2D{RealT},
         CompressibleEulerEquations3D{RealT},
         IdealGlmMhdEquations1D{RealT},
         IdealGlmMhdEquations2D{RealT},
         IdealGlmMhdEquations3D{RealT},
         LatticeBoltzmannEquations2D{RealT, typeof(Trixi.collision_bgk)},
         LatticeBoltzmannEquations3D{RealT, typeof(Trixi.collision_bgk)})
    end

    function basis_type_dgsem(RealT, nnodes_)
        LobattoLegendreBasis{RealT, nnodes_,
                             # VectorT
                             StaticArrays.SVector{nnodes_, RealT},
                             # InverseVandermondeLegendre
                             Matrix{RealT},
                             # BoundaryMatrix
                             #StaticArrays.SArray{Tuple{nnodes_,2},RealT,2,2*nnodes_},
                             Matrix{RealT},
                             # DerivativeMatrix
                             #StaticArrays.SArray{Tuple{nnodes_,nnodes_},RealT,2,nnodes_^2},
                             Matrix{RealT}}
    end

    function mortar_type_dgsem(RealT, nnodes_)
        LobattoLegendreMortarL2{RealT, nnodes_,
                                # ForwardMatrix
                                #StaticArrays.SArray{Tuple{nnodes_,nnodes_},RealT,2,nnodes_^2},
                                Matrix{RealT},
                                # ReverseMatrix
                                # StaticArrays.SArray{Tuple{nnodes_,nnodes_},RealT,2,nnodes_^2},
                                Matrix{RealT}}
    end

    function analyzer_type_dgsem(RealT, nnodes_)
        polydeg = nnodes_ - 1
        nnodes_analysis = 2 * polydeg + 1
        LobattoLegendreAnalyzer{RealT, nnodes_analysis,
                                # VectorT
                                StaticArrays.SVector{nnodes_analysis, RealT},
                                # Vandermonde
                                Array{RealT, 2}}
    end

    function adaptor_type_dgsem(RealT, nnodes_)
        LobattoLegendreAdaptorL2{RealT, nnodes_,
                                 # ForwardMatrix
                                 StaticArrays.SArray{Tuple{nnodes_, nnodes_}, RealT, 2,
                                                     nnodes_^2},
                                 # Matrix{RealT},
                                 # ReverseMatrix
                                 StaticArrays.SArray{Tuple{nnodes_, nnodes_}, RealT, 2,
                                                     nnodes_^2}
                                 # Matrix{RealT},
                                 }
    end

    # Constructors: mesh
    for RealT in (Int, Float64)
        @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                      NamedTuple{(:initial_refinement_level, :n_cells_max),
                                                 Tuple{Int, Int}}, Type{TreeMesh},
                                      RealT, RealT})
        @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                      NamedTuple{(:initial_refinement_level, :n_cells_max),
                                                 Tuple{Int, Int}}, Type{TreeMesh},
                                      Tuple{RealT}, Tuple{RealT}})
        @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                      NamedTuple{(:initial_refinement_level, :n_cells_max),
                                                 Tuple{Int, Int}}, Type{TreeMesh},
                                      Tuple{RealT, RealT}, Tuple{RealT, RealT}})
        @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                      NamedTuple{(:initial_refinement_level, :n_cells_max),
                                                 Tuple{Int, Int}}, Type{TreeMesh},
                                      Tuple{RealT, RealT, RealT},
                                      Tuple{RealT, RealT, RealT}})
    end
    for TreeType in (SerialTree, ParallelTree), NDIMS in 1:3
        @assert Base.precompile(Tuple{typeof(Trixi.initialize!),
                                      TreeMesh{NDIMS, TreeType{NDIMS}, Float64}, Int,
                                      Tuple{},
                                      Tuple{}})
        @assert Base.precompile(Tuple{typeof(Trixi.save_mesh_file),
                                      TreeMesh{NDIMS, TreeType{NDIMS}, Float64}, String,
                                      Int})
    end

    # Constructors: linear advection
    for RealT in (Float64,)
        @assert Base.precompile(Tuple{Type{LinearScalarAdvectionEquation1D}, RealT})
        @assert Base.precompile(Tuple{Type{LinearScalarAdvectionEquation2D}, RealT, RealT})
        @assert Base.precompile(Tuple{Type{LinearScalarAdvectionEquation2D},
                                      Tuple{RealT, RealT}})
        @assert Base.precompile(Tuple{Type{LinearScalarAdvectionEquation3D}, RealT, RealT,
                                      RealT})
        @assert Base.precompile(Tuple{Type{LinearScalarAdvectionEquation3D},
                                      Tuple{RealT, RealT, RealT}})
    end

    # Constructors: hyperbolic diffusion
    for RealT in (Float64,)
        @assert Base.precompile(Tuple{Type{HyperbolicDiffusionEquations1D}})
        @assert Base.precompile(Tuple{Type{HyperbolicDiffusionEquations2D}})
        @assert Base.precompile(Tuple{Type{HyperbolicDiffusionEquations3D}})
    end

    # Constructors: Euler
    for RealT in (Float64,)
        @assert Base.precompile(Tuple{Type{CompressibleEulerEquations1D}, RealT})
        @assert Base.precompile(Tuple{Type{CompressibleEulerEquations2D}, RealT})
        @assert Base.precompile(Tuple{Type{CompressibleEulerEquations3D}, RealT})
    end

    # Constructors: MHD
    for RealT in (Float64,)
        @assert Base.precompile(Tuple{Type{IdealGlmMhdEquations1D}, RealT})
        @assert Base.precompile(Tuple{Type{IdealGlmMhdEquations2D}, RealT})
        @assert Base.precompile(Tuple{Type{IdealGlmMhdEquations3D}, RealT})
    end

    # Constructors: LBM
    for RealT in (Float64,)
        @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                      NamedTuple{(:Ma, :Re), Tuple{RealT, RealT}},
                                      Type{LatticeBoltzmannEquations2D}})
        @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                      NamedTuple{(:Ma, :Re), Tuple{RealT, Int}},
                                      Type{LatticeBoltzmannEquations2D}})
        @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                      NamedTuple{(:Ma, :Re), Tuple{RealT, RealT}},
                                      Type{LatticeBoltzmannEquations3D}})
        @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                      NamedTuple{(:Ma, :Re), Tuple{RealT, Int}},
                                      Type{LatticeBoltzmannEquations3D}})
    end

    # Constructors of the basis are inherently type-unstable since we pass integers
    # and use their values as parameters of static arrays.
    # Nevertheless, we can still precompile methods used to construct the bases.
    Base.precompile(Tuple{Type{LobattoLegendreBasis}, Int})
    for RealT in (Float64,)
        Base.precompile(Tuple{Type{LobattoLegendreBasis}, RealT, Int})
        @assert Base.precompile(Tuple{typeof(Trixi.calc_dhat), Vector{RealT},
                                      Vector{RealT}})
        @assert Base.precompile(Tuple{typeof(Trixi.calc_dsplit), Vector{RealT},
                                      Vector{RealT}})
        @assert Base.precompile(Tuple{typeof(Trixi.polynomial_derivative_matrix),
                                      Vector{RealT}})
        @assert Base.precompile(Tuple{typeof(Trixi.polynomial_interpolation_matrix),
                                      Vector{RealT}, Vector{RealT}})
        @assert Base.precompile(Tuple{typeof(Trixi.barycentric_weights), Vector{RealT}})
        @assert Base.precompile(Tuple{typeof(Trixi.calc_lhat), RealT, Vector{RealT},
                                      Vector{RealT}})
        @assert Base.precompile(Tuple{typeof(Trixi.lagrange_interpolating_polynomials),
                                      RealT, Vector{RealT}, Vector{RealT}})
        @assert Base.precompile(Tuple{typeof(Trixi.calc_q_and_l), Int, RealT})
        @assert Base.precompile(Tuple{typeof(Trixi.legendre_polynomial_and_derivative), Int,
                                      RealT})
        @assert Base.precompile(Tuple{typeof(Trixi.vandermonde_legendre), Vector{RealT}})
    end
    @assert Base.precompile(Tuple{typeof(Trixi.gauss_lobatto_nodes_weights), Int})
    @assert Base.precompile(Tuple{typeof(Trixi.gauss_nodes_weights), Int})
    @assert Base.precompile(Tuple{typeof(Trixi.calc_forward_upper), Int})
    @assert Base.precompile(Tuple{typeof(Trixi.calc_forward_lower), Int})
    @assert Base.precompile(Tuple{typeof(Trixi.calc_reverse_upper), Int,
                                  Val{:gauss}})
    @assert Base.precompile(Tuple{typeof(Trixi.calc_reverse_lower), Int,
                                  Val{:gauss}})
    @assert Base.precompile(Tuple{typeof(Trixi.calc_reverse_upper), Int,
                                  Val{:gauss_lobatto}})
    @assert Base.precompile(Tuple{typeof(Trixi.calc_reverse_lower), Int,
                                  Val{:gauss_lobatto}})

    # Constructors: mortars, analyzers, adaptors
    for RealT in (Float64,), polydeg in 1:7
        nnodes_ = polydeg + 1
        basis_type = basis_type_dgsem(RealT, nnodes_)
        @assert Base.precompile(Tuple{typeof(Trixi.MortarL2), basis_type})
        @assert Base.precompile(Tuple{Type{Trixi.SolutionAnalyzer}, basis_type})
        @assert Base.precompile(Tuple{Type{Trixi.AdaptorL2}, basis_type})
    end

    # Constructors: callbacks
    @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                  NamedTuple{(:analysis_interval,), Tuple{Int}},
                                  Type{AliveCallback}})
    for RealT in (Float64,)
        @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                      NamedTuple{(:cfl,), Tuple{RealT}},
                                      Type{StepsizeCallback}})
        @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                      NamedTuple{(:glm_scale, :cfl), Tuple{RealT, RealT}},
                                      Type{GlmSpeedCallback}})
    end
    @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                  NamedTuple{(:interval, :save_final_restart),
                                             Tuple{Int, Bool}}, Type{SaveRestartCallback}})
    @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                  NamedTuple{(:interval, :save_initial_solution,
                                              :save_final_solution, :solution_variables),
                                             Tuple{Int, Bool, Bool, typeof(cons2cons)}},
                                  Type{SaveSolutionCallback}})
    @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),
                                  NamedTuple{(:interval, :save_initial_solution,
                                              :save_final_solution, :solution_variables),
                                             Tuple{Int, Bool, Bool, typeof(cons2prim)}},
                                  Type{SaveSolutionCallback}})
    # TODO: AnalysisCallback?
    # for RealT in (Float64,), polydeg in 1:7
    #   nnodes_ = polydeg + 1
    #   nnodes_analysis = 2*polydeg + 1
    # @assert Base.precompile(Tuple{Type{AnalysisCallback},RealT,Int,Bool,String,String,Trixi.LobattoLegendreAnalyzer{RealT,nnodes_analysis,Array{RealT,2}},Array{Symbol,1},Tuple{typeof(Trixi.entropy_timederivative),typeof(entropy)},StaticArrays.SArray{Tuple{1},RealT,1,1}})
    # We would need to use all special cases instead of
    # Function,Trixi.AbstractVolumeIntegral
    # for equations_type in equations_types(RealT)
    #   @assert Base.precompile(Tuple{Core.kwftype(typeof(Trixi.Type)),NamedTuple{(:interval, :extra_analysis_integrals),Tuple{Int,Tuple{typeof(entropy)}}},Type{AnalysisCallback},equations_type,DG{RealT,LobattoLegendreBasis{RealT,nnodes_,StaticArrays.SVector{nnodes_,RealT},Array{RealT,2},StaticArrays.SArray{Tuple{4,2},RealT,2,2*nnodes_},StaticArrays.SArray{Tuple{nnodes_,nnodes_},RealT,2,nnodes_^2}},Trixi.LobattoLegendreMortarL2{RealT,nnodes_,StaticArrays.SArray{Tuple{nnodes_,nnodes_},RealT,2,nnodes_^2}},Function,Trixi.AbstractVolumeIntegral}})
    # end
    # end
    @assert Base.precompile(Tuple{typeof(SummaryCallback)})
    @assert Base.precompile(Tuple{typeof(summary_box), Base.TTY, String,
                                  Vector{Pair{String, Any}}})
    # TODO: AMRCallback, ControllerThreeLevel, indicators

    # init_elements, interfaces, etc.
    for RealT in (Float64,), polydeg in 1:7
        uEltype = RealT
        nnodes_ = polydeg + 1
        mortar_type = mortar_type_dgsem(RealT, nnodes_)

        # 1D, serial
        @assert Base.precompile(Tuple{typeof(Trixi.init_boundaries), Array{Int, 1},
                                      TreeMesh{1, Trixi.SerialTree{1}, RealT},
                                      Trixi.ElementContainer1D{RealT, uEltype}})
        @assert Base.precompile(Tuple{typeof(Trixi.init_interfaces), Array{Int, 1},
                                      TreeMesh{1, Trixi.SerialTree{1}, RealT},
                                      Trixi.ElementContainer1D{RealT, uEltype}})
        @assert Base.precompile(Tuple{typeof(Trixi.save_mesh_file),
                                      TreeMesh{1, Trixi.SerialTree{1}, RealT}, String})

        # 2D, serial
        @assert Base.precompile(Tuple{typeof(Trixi.init_boundaries), Array{Int, 1},
                                      TreeMesh{2, Trixi.SerialTree{2}, RealT},
                                      Trixi.ElementContainer2D{RealT, uEltype}})
        @assert Base.precompile(Tuple{typeof(Trixi.init_interfaces), Array{Int, 1},
                                      TreeMesh{2, Trixi.SerialTree{2}, RealT},
                                      Trixi.ElementContainer2D{RealT, uEltype}})
        @assert Base.precompile(Tuple{typeof(Trixi.init_mortars), Array{Int, 1},
                                      TreeMesh{2, Trixi.SerialTree{2}, RealT},
                                      Trixi.ElementContainer2D{RealT, uEltype},
                                      mortar_type})
        @assert Base.precompile(Tuple{typeof(Trixi.save_mesh_file),
                                      TreeMesh{2, Trixi.SerialTree{2}, RealT}, String})

        # 2D, parallel
        @assert Base.precompile(Tuple{typeof(Trixi.init_boundaries), Array{Int, 1},
                                      TreeMesh{2, Trixi.ParallelTree{2}, RealT},
                                      Trixi.ElementContainer2D{RealT, uEltype}})
        @assert Base.precompile(Tuple{typeof(Trixi.init_interfaces), Array{Int, 1},
                                      TreeMesh{2, Trixi.ParallelTree{2}, RealT},
                                      Trixi.ElementContainer2D{RealT, uEltype}})
        @assert Base.precompile(Tuple{typeof(Trixi.init_mortars), Array{Int, 1},
                                      TreeMesh{2, Trixi.ParallelTree{2}, RealT},
                                      Trixi.ElementContainer2D{RealT, uEltype},
                                      mortar_type})
        @assert Base.precompile(Tuple{typeof(Trixi.init_mpi_interfaces), Array{Int, 1},
                                      TreeMesh{2, Trixi.ParallelTree{2}, RealT},
                                      Trixi.ElementContainer2D{RealT, uEltype}})
        @assert Base.precompile(Tuple{typeof(Trixi.save_mesh_file),
                                      TreeMesh{2, Trixi.ParallelTree{2}, RealT}, String})

        # 3D, serial
        @assert Base.precompile(Tuple{typeof(Trixi.init_boundaries), Array{Int, 1},
                                      TreeMesh{3, Trixi.SerialTree{3}, RealT},
                                      Trixi.ElementContainer3D{RealT, uEltype}})
        @assert Base.precompile(Tuple{typeof(Trixi.init_interfaces), Array{Int, 1},
                                      TreeMesh{3, Trixi.SerialTree{3}, RealT},
                                      Trixi.ElementContainer3D{RealT, uEltype}})
        @assert Base.precompile(Tuple{typeof(Trixi.init_mortars), Array{Int, 1},
                                      TreeMesh{3, Trixi.SerialTree{3}, RealT},
                                      Trixi.ElementContainer3D{RealT, uEltype},
                                      mortar_type})
        @assert Base.precompile(Tuple{typeof(Trixi.save_mesh_file),
                                      TreeMesh{3, Trixi.SerialTree{3}, RealT}, String})
    end

    # various `show` methods
    for RealT in (Float64,)
        # meshes
        for NDIMS in 1:3
            # serial
            @assert Base.precompile(Tuple{typeof(show), Base.TTY,
                                          TreeMesh{NDIMS, Trixi.SerialTree{NDIMS}, RealT}})
            @assert Base.precompile(Tuple{typeof(show), IOContext{Base.TTY},
                                          MIME"text/plain",
                                          TreeMesh{NDIMS, Trixi.SerialTree{NDIMS}, RealT}})
            # parallel
            @assert Base.precompile(Tuple{typeof(show), Base.TTY,
                                          TreeMesh{NDIMS, Trixi.ParallelTree{NDIMS}, RealT}})
            @assert Base.precompile(Tuple{typeof(show), IOContext{Base.TTY},
                                          MIME"text/plain",
                                          TreeMesh{NDIMS, Trixi.ParallelTree{NDIMS}, RealT}})
        end

        # equations
        for eq_type in equations_types(RealT)
            @assert Base.precompile(Tuple{typeof(show), Base.TTY, eq_type})
            @assert Base.precompile(Tuple{typeof(show), IOContext{Base.TTY},
                                          MIME"text/plain", eq_type})
        end

        # mortars, analyzers, adaptors, DG
        for polydeg in 1:1
            nnodes_ = polydeg + 1
            basis_type = basis_type_dgsem(RealT, nnodes_)
            mortar_type = mortar_type_dgsem(RealT, nnodes_)
            analyzer_type = analyzer_type_dgsem(RealT, nnodes_)
            adaptor_type = adaptor_type_dgsem(RealT, nnodes_)

            @assert Base.precompile(Tuple{typeof(show), Base.TTY, basis_type})
            @assert Base.precompile(Tuple{typeof(show), IOContext{Base.TTY},
                                          MIME"text/plain", basis_type})

            @assert Base.precompile(Tuple{typeof(show), Base.TTY, mortar_type})
            @assert Base.precompile(Tuple{typeof(show), IOContext{Base.TTY},
                                          MIME"text/plain", mortar_type})

            @assert Base.precompile(Tuple{typeof(show), Base.TTY, analyzer_type})
            @assert Base.precompile(Tuple{typeof(show), IOContext{Base.TTY},
                                          MIME"text/plain", analyzer_type})

            @assert Base.precompile(Tuple{typeof(show), Base.TTY, adaptor_type})
            @assert Base.precompile(Tuple{typeof(show), IOContext{Base.TTY},
                                          MIME"text/plain", adaptor_type})

            # we could also use more numerical fluxes and volume integral types here
            @assert Base.precompile(Tuple{typeof(show), Base.TTY,
                                          DG{basis_type, mortar_type,
                                             typeof(flux_lax_friedrichs),
                                             VolumeIntegralWeakForm}})
            @assert Base.precompile(Tuple{typeof(show), IOContext{Base.TTY},
                                          MIME"text/plain",
                                          DG{basis_type, mortar_type,
                                             typeof(flux_lax_friedrichs),
                                             VolumeIntegralWeakForm}})
        end

        # semidiscretizations
        @assert Base.precompile(Tuple{typeof(show), IOContext{Base.TTY}, MIME"text/plain",
                                      SemidiscretizationHyperbolic})

        # We do not precompile callbacks since they are based on
        # SciML structures like `DiscreteCallback` that may change their
        # type signatures in non-breaking releases.
    end

    @assert Base.precompile(Tuple{typeof(init_mpi)})
    @assert Base.precompile(Tuple{typeof(init_p4est)})

    # The following precompile statements do not seem to be taken
    # # `multiply_dimensionwise!` as used in the analysis callback
    # for RealT in (Float64,)
    #   # 1D version
    #   @assert Base.precompile(Tuple{typeof(multiply_dimensionwise!),Array{RealT, 2},Matrix{RealT},SubArray{RealT, 2, Array{RealT, 3}, Tuple{Base.Slice{Base.OneTo{Int}}, Base.Slice{Base.OneTo{Int}}, Int}, true}})
    #   # 2D version
    #   @assert Base.precompile(Tuple{typeof(multiply_dimensionwise!),Array{RealT, 3},Matrix{RealT},SubArray{RealT, 3, Array{RealT, 4}, Tuple{Base.Slice{Base.OneTo{Int}}, Base.Slice{Base.OneTo{Int}}, Base.Slice{Base.OneTo{Int}}, Int}, true},Array{RealT, 3}})
    #   # 3D version
    #   @assert Base.precompile(Tuple{typeof(multiply_dimensionwise!),Array{RealT, 4},Matrix{RealT},SubArray{RealT, 4, Array{RealT, 5}, Tuple{Base.Slice{Base.OneTo{Int}}, Base.Slice{Base.OneTo{Int}}, Base.Slice{Base.OneTo{Int}}, Base.Slice{Base.OneTo{Int}}, Int}, true},Array{RealT, 4},Array{RealT, 4}})
    # end

    return nothing
end

# Explicit precompilation including running code
using PrecompileTools: @setup_workload, @compile_workload

@setup_workload begin
    # Setup code can go here

    @compile_workload begin
        # Everything inside this block will run at precompile time, saving the
        # binary code to a cache in newer versions of Julia.
        DGSEM(3)
    end
end