Julia precision issues

### A Pluto.jl notebook ###
# v0.17.7

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ 67299d01-feec-4151-a450-a1f1e702da6c
using ChangePrecision, HypertextLiteral, LaTeXStrings, LinearAlgebra, Plots, PlutoUI, Statistics

# ╔═╡ ac1056bc-aab8-43dc-8cdb-bcabae9d5e04
gr()

# ╔═╡ 3665ac78-a5d3-40ca-bc56-64880b459344
md"### ``\Omega(n^2)`` construction for ICP in ``\mathbb{R}``"

# ╔═╡ 51c2da8b-a609-4916-a3fd-55d12f9269fd
setprecision(2000)

# ╔═╡ 35363121-5cdf-488a-a0b3-dd5fba91215c
n::BigFloat = 8

# ╔═╡ a07283f0-f2cd-4054-b45b-5c63281dfc37
md"Zoom in on **Linear Shifter**: $(@bind zoom CheckBox())"

# ╔═╡ 26a1ac35-5d88-477d-9b12-ead4ffc79220
md"## Helpers & Miscellaneous"

# ╔═╡ 96161c01-336c-4012-b502-9a2b31961aea
md"#### Widgets"

# ╔═╡ a0512ff6-6816-4368-ad05-92d7145c013b
struct Region
    A::Vector{BigFloat}
    B::Vector{BigFloat}
    width::BigFloat # largest (a, b) distance

    function Region(A::Vector, B::Vector)
        @changeprecision BigFloat begin
            width::BigFloat = maximum([abs(a-b) for a ∈ A, b ∈ B])
            return new(sort(A), sort(B), width)
        end
    end
end

# ╔═╡ 3c374a74-9f59-4814-bfdb-25c456ad30a6
struct ICPConstruction
    regions::Vector{Region}
    A::Vector{BigFloat} # point set A
    B::Vector{BigFloat} # point set B
    δ::BigFloat # largest (a, b) distance within any region

    "Assembles full ICP construction with A and B point sets (vectors)."
    function ICPConstruction(regions::Vector{Region})
        @changeprecision BigFloat begin
            # extract, concatenate, and sort overall A and B from regions
            A = reduce(vcat, map(r -> r.A, regions)) |> sort
            B = reduce(vcat, map(r -> r.B, regions)) |> sort
            δ = reduce(vcat, map(r -> r.width, regions)) |> maximum
            return new(regions, A, B, δ)
        end
    end
end

# ╔═╡ 76cb3d7f-3f7c-4b73-a6d3-1f5c9f460475
# Augmented Linear Shifter
function AugmentedLinearShifter(n::BigFloat)::ICPConstruction
    @changeprecision BigFloat begin
        # width of augmented linear shifter is (2n + 1)ℓ - 1 / k^n
        k::BigFloat = 3n + 2
        ℓ::BigFloat = sum([1 / k^(j-1) for j ∈ 1:n+1])

        # Define A
        A::Vector{BigFloat} = [-2i * ℓ for i ∈ 0:n]

        # Define B
        b₀::BigFloat = 0.0
        b(i) = sum([1 / k^(j-1) for j ∈ 1:i])
        bᵢ::Vector{BigFloat} = [b(i) for i ∈ 1:n]
        B::Vector{BigFloat} = vcat(b₀, bᵢ)

        # Define Linear Shifter
        linear_shifter = Region(A, B)
        return ICPConstruction([linear_shifter])
    end
end;

# ╔═╡ 12d65dbf-9aa7-46e4-886b-ee34ade546a7
struct Redirector
    regions::Tuple{Region, Region}
    A::Vector{BigFloat} # A₁ ∪ A₂
    B::Vector{BigFloat} # B₁ ∪ B₂
    v::BigFloat
    y::BigFloat

    function Redirector(v::BigFloat, y::BigFloat, k::BigFloat)
        @changeprecision BigFloat begin
            # Region 1
            a::BigFloat = 1/2 * k * v - y # a is y to the left of the (b₁ b₂) midpoint
            b₁::BigFloat = 0
            b₂::BigFloat = k * v
            A₁ = [a]
            B₁ = [b₁, b₂]
            R₁ = Region(A₁, B₁)

            # Region 2
            a′::BigFloat = 0.0
            A₂ = [a′]
            B₂ = [a′ + 1/2]
            R₂ = Region(A₂, B₂)

            regions = (R₁, R₂)
            A = reduce(vcat, map(r -> r.A, regions)) |> sort
            B = reduce(vcat, map(r -> r.B, regions)) |> sort

            return new((R₁, R₂), A, B, v, y)
        end
    end
end

# ╔═╡ 3fd94606-c565-4bde-aafb-a67a2517e93b
begin
    function add_region(c::ICPConstruction, new::Region)::ICPConstruction
        @changeprecision BigFloat begin
            δ = maximum([c.δ, new.width])
            min_old = minimum(vcat(c.A, c.B))
            max_new = maximum(vcat(new.A, new.B))
            shift = abs(min_old - max_new) + 3δ + 1

            A′ = new.A .- shift
            B′ = new.B .- shift
            regions = vcat(c.regions, Region(A′, B′))
            return ICPConstruction(regions)
        end
    end

    md"""
        ``\texttt{add\_region(c::ICPConstruction, new::Region)::ICPConstruction}``

        Adds a region to an ICP construction while maintaining ``>3\delta`` distance between regions, where ``\delta`` is the largest ``(a, b)`` distance within any region. Returns a new, updated ICP construction.

        ---
        """
end

# ╔═╡ a5f30ef1-9c98-4a4f-ab89-9e43adb071d3
md"#### ICP"

# ╔═╡ 6d4927de-a902-414e-94ed-922dffdfeef1
begin
    function icp1d(construction::ICPConstruction; k = 0)
        @changeprecision BigFloat begin
            A::Vector{BigFloat} = copy(construction.A)
            B::Vector{BigFloat} = copy(construction.B)

            # generate k-d tree for efficient nearest neighbour search
            # kdtree = KDTree(BigFloat.(B'))

            t::BigFloat = 0
            # correspondences::Vector{Int64} = nn(kdtree, BigFloat.(A'))[1]
            correspondences::Vector{Int64} = []
            for a ∈ A
                neighbor = argmin(abs.(B .- a))
                push!(correspondences, neighbor)
            end

            # Remember transformations for visualization
            ts::Vector{BigFloat} = []
            cs::Vector{Vector{Int64}} = []

            while true
                # remember iteration state for visualization
                push!(ts, t)
                push!(cs, copy(correspondences))

                # find nearest neighbours
                BNeighbours = @view B[correspondences]

                # calculate mean for each point cloud
                a0::BigFloat = k == 0 ? mean(A) : sum(A) / k
                b0::BigFloat = k == 0 ? mean(BNeighbours) : sum(BNeighbours) / k

                # compute transformations
                t = b0 - a0
                A .+= t

                # compute new correspondences
                # correspondences = nn(kdtree, A')[1]
                correspondences = []
                for a ∈ A
                    neighbor = argmin(abs.(B .- a))
                    push!(correspondences, neighbor)
                end

                # terminate if nearest neighbours don't change
                if correspondences == cs[end]
                    push!(ts, t)
                    break
                end
            end

            return ts, cs
        end
    end

    md"""
    ``\texttt{icp1d(A, B)}``

    Compute the one-dimensional ICP algorithm.

    ---
    """
end

# ╔═╡ 9d3bd673-29cd-4b3c-aab8-f1a5c2a1c229
function run_full_construction(n::BigFloat)
    @changeprecision BigFloat begin
        k::BigFloat = 3n + 2
        ℓ::BigFloat = sum([1 / k^(j-1) for j ∈ 1:n+1])

        construction = AugmentedLinearShifter(n);
        redirectors = [Redirector(ℓ + 1, (2i + 1)ℓ, k) for i ∈ 0:n-1]
        redirector_regions = map(r -> collect(r.regions), redirectors) |> Iterators.flatten |> collect

        for region ∈ redirector_regions
            construction = add_region(construction, region)
        end

        # determine kickoff translation
        x₁::BigFloat = icp1d(construction, k=k)[1][2]

        a′::BigFloat = 0.0
        b′::BigFloat = a′ + (1.0 - x₁)k
        kicker_region = Region([a′], [b′])

        # complete construction with kicker region
        construction = add_region(construction, kicker_region)
        @assert length(construction.A) == k "k must equal |A|"

        # run ICP on fill construction
        translations, correspondences = icp1d(construction)
        return construction, translations, correspondences
    end
end

# ╔═╡ b749c880-2316-4699-bf71-ec0b9146e93e
construction, t, c = run_full_construction(n);

# ╔═╡ 873d9064-289b-4886-a944-6043e4eb237c
md"#### Plotting functions"

# ╔═╡ a755ff61-6487-43e2-a155-b3767965bf52
begin
    function plot_icp1d(
        construction::ICPConstruction;
        translations::Vector{BigFloat} = nothing,
        correspondences::Vector{Vector{Int64}} = nothing,
        iteration::Int64 = nothing,
        width::Int64 = 650,
        zoom::Bool
    )
        A = copy(construction.A)
        B = copy(construction.B)
        total_iterations = isnothing(translations) ? 1 : length(translations)
        ylim = (-1, 2)
        m, n = length(A), length(B)

        linear_shifter_points = [construction.regions[1].A, construction.regions[1].B] |> Iterators.flatten |> collect
        xmin = minimum(linear_shifter_points)*0.99
        xmax = maximum(linear_shifter_points)*1.00001
        xlim = zoom ? [xmin, xmax] : [A[1]*.99, B[end]*1.00001]

        # Transform A
        A_transformed = A .+ (isnothing(translations) ? 0 : sum(translations[1:iteration]))

        # Red line for A
        p = plot(
            A_transformed,
            ones(m),
            color="#FF0068",
            opacity=0.4,
            title=isnothing(iteration) ? nothing : "ICP iteration $iteration of $total_iterations",
            style=:dash,
            label=false,
            xlim=xlim,
            ylim=ylim,
            yaxis=nothing,
            xaxis=nothing,
            size=(width, 200),
            legend=nothing,
            grid=nothing
        )

        # Correspondences
        if !isnothing(correspondences)
            max_cs = minimum([total_iterations-1, iteration])

            for j ∈ 1:m
                a = [A_transformed[j], 1]
                b = [B[correspondences[max_cs][j]], 0]

                plot!(
                    [a[1], b[1]],
                    [a[2], b[2]],
                    color=iteration < total_iterations ? "lightgrey" : "lightgreen",
                    labels = j == 1 ? "NN pair" : false
                )
            end
        end

        boundaries = [(B[k] + B[k+1]) / 2 for k in 1:n-1]

        if zoom
            latex_labels_B = map(x->latexstring(x), ["b_{$i}" for i in 1:n])
            annotate!([(B[i], -0.5, (latex_labels_B[i], 8, "#4A3D90", :bottom)) for i in 1:n])

            latex_labels_A = map(x->latexstring(x), ["a_{$i}" for i in 1:m])
            annotate!([(A_transformed[i], 1.4, (latex_labels_A[i], 8, "#FF0068", :top)) for i in 1:m])
        end

        # Point markers for A
        scatter!(A_transformed, ones(m), color="#FF0068", label="A")

        # Blue line for B
        plot!(B, zeros(n), color="#4A3D90", opacity=0.4, style=:dash, label=false)

        # Point markers for B
        scatter!(B, zeros(n), color="#4A3D90", label="B")

        p
    end

    md"""
    ``\texttt{plot\_icp1d(A, B; translations, correspondences, iteration, showlabels=true, width=650)}``

    Plot the one-dimensional ICP algorithm.

    ---
    """
end

# ╔═╡ 43b83809-65cc-4325-8880-406baa5b7ab3
begin
    struct LabeledSlider
        range::AbstractRange
        default::Number
    end

    function Base.show(io::IO, ::MIME"text/html", slider::LabeledSlider)
        print(io, """
            <input type="range"
            min="$(first(slider.range))"
            step="$(step(slider.range))"
            max="$(last(slider.range))"
            value="$(slider.default)"
            style='width: 80%;'
            oninput="this.nextElementSibling.value=this.value">
            <output>$(slider.default)</output>""")
    end
    md"Define ``\texttt{LabeledSlider}``"
end

# ╔═╡ c4918491-662a-4065-9238-363cf73ff3e2
md"``i = ``$(@bind i LabeledSlider(1:length(t), 1))"

# ╔═╡ d593b47a-efd4-4fa2-9bb1-b944970d1a8a
plot_icp1d(construction; translations=t, correspondences=c, iteration=i, width=1000, zoom=zoom)

# ╔═╡ 19080b1a-7b10-4b4f-8971-34483a9629fa
md"#### Increase Pluto notebook width"

# ╔═╡ ff051e76-c5b8-4607-b75e-4f867f77d5c9
@bind screenWidth @htl("<div><script>var div = currentScript.parentElement; div.value = screen.width</script></div>")

# ╔═╡ 673fa13b-bf20-4879-b1f8-e3220bb649d7
@htl("<style>pluto-notebook { margin: auto; width: $(min(1000, screenWidth*0.9))px; }</style>")

# ╔═╡ 00000000-0000-0000-0000-000000000001
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git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

[[deps.SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[deps.StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "2884859916598f974858ff01df7dfc6c708dd895"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.3.3"

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[deps.StatsAPI]]
git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.2.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "51383f2d367eb3b444c961d485c565e4c0cf4ba0"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.14"

[[deps.StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "d21f2c564b21a202f4677c0fba5b5ee431058544"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.4"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.1"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unzip]]
git-tree-sha1 = "34db80951901073501137bdbc3d5a8e7bbd06670"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.1.2"

[[deps.Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
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# ╠═b749c880-2316-4699-bf71-ec0b9146e93e
# ╟─c4918491-662a-4065-9238-363cf73ff3e2
# ╟─a07283f0-f2cd-4054-b45b-5c63281dfc37
# ╟─d593b47a-efd4-4fa2-9bb1-b944970d1a8a
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# ╠═3c374a74-9f59-4814-bfdb-25c456ad30a6
# ╠═a0512ff6-6816-4368-ad05-92d7145c013b
# ╠═76cb3d7f-3f7c-4b73-a6d3-1f5c9f460475
# ╠═12d65dbf-9aa7-46e4-886b-ee34ade546a7
# ╠═3fd94606-c565-4bde-aafb-a67a2517e93b
# ╟─a5f30ef1-9c98-4a4f-ab89-9e43adb071d3
# ╠═6d4927de-a902-414e-94ed-922dffdfeef1
# ╟─873d9064-289b-4886-a944-6043e4eb237c
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# ╟─43b83809-65cc-4325-8880-406baa5b7ab3
# ╟─19080b1a-7b10-4b4f-8971-34483a9629fa
# ╠═ff051e76-c5b8-4607-b75e-4f867f77d5c9
# ╠═673fa13b-bf20-4879-b1f8-e3220bb649d7
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002