Fast partitions

bench.jl

import Random
using BenchmarkTools
Random.seed!(0)
println("branch, type, len, dims, desc, time")
for n in round.(Int, 10.0.^(0.5:0.5:5))
    for T in (Int8, Int32, Int64)
        for (desc, dims) in (("1d", (100n,)),
                             ("2d (wide)", (10, 10n)),
                             ("2d (tall)", (10n, 10)),
                             (n > 10 ? (("3d (wide)", (10, 10, n)),
                                        ("3d (tall)", (n, 10, 10)),) : ())...)
            a = rand(T(0):T(4), dims)
            b = @benchmark $a .== $(T(0))
            println("$(Base.GIT_VERSION_INFO.branch)-$(Base.GIT_VERSION_INFO.commit_short), $T, $(100n), $(Base.dims2string(dims)), $desc, $(minimum(b).time)")
        end
    end
end

change.csv

diff.svg

Manifest.toml

# This file is machine-generated - editing it directly is not advised

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[[SpecialFunctions]]
deps = ["BinDeps", "BinaryProvider", "Libdl", "Test"]
git-tree-sha1 = "0b45dc2e45ed77f445617b99ff2adf0f5b0f23ea"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "0.7.2"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "db23bbf50064c582b6f2b9b043c8e7e98ea8c0c6"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "0.11.0"

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

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics"]
git-tree-sha1 = "c53e809e63fe5cf5de13632090bc3520649c9950"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.32.0"

[[StatsFuns]]
deps = ["Rmath", "SpecialFunctions", "Test"]
git-tree-sha1 = "b3a4e86aa13c732b8a8c0ba0c3d3264f55e6bb3e"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "0.8.0"

[[StatsPlots]]
deps = ["Clustering", "DataStructures", "DataValues", "Distributions", "Interpolations", "KernelDensity", "Observables", "Plots", "RecipesBase", "Reexport", "StatsBase", "Tables", "Widgets"]
git-tree-sha1 = "9f3f096a310f25debaca9dbe6b4e0df7bb428fd0"
uuid = "f3b207a7-027a-5e70-b257-86293d7955fd"
version = "0.12.0"

[[SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "b1ad568ba658d8cbb3b892ed5380a6f3e781a81e"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.0"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "aaed7b3b00248ff6a794375ad6adf30f30ca5591"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "0.2.11"

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

[[URIParser]]
deps = ["Test", "Unicode"]
git-tree-sha1 = "6ddf8244220dfda2f17539fa8c9de20d6c575b69"
uuid = "30578b45-9adc-5946-b283-645ec420af67"
version = "0.4.0"

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

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

[[VersionParsing]]
deps = ["Compat"]
git-tree-sha1 = "c9d5aa108588b978bd859554660c8a5c4f2f7669"
uuid = "81def892-9a0e-5fdd-b105-ffc91e053289"
version = "1.1.3"

[[WeakRefStrings]]
deps = ["Random", "Test"]
git-tree-sha1 = "9a0bb82eede528debe631b642eeb48a631a69bc2"
uuid = "ea10d353-3f73-51f8-a26c-33c1cb351aa5"
version = "0.6.1"

[[Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "fc0feda91b3fef7fe6948ee09bb628f882b49ca4"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.2"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "Test"]
git-tree-sha1 = "21772c33b447757ec7d3e61fcdfb9ea5c47eedcf"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.4.1"

master.csv

plot.jl

using CSV, Plots, StatsPlots

master = CSV.read("master.csv", normalizenames=true)
change = CSV.read("change.csv", normalizenames=true)

df = vcat(master, change)

p = @df df[df.desc .== " 1d",:] scatter(:len, :time./1e3, group=(:branch), xscale=:log10, yscale=:log10, legend=:topleft, ylabel="microseconds", xlabel="array length", title="1-dimensional")
savefig(p, "1d.svg")

p = scatter(parse.(Int, first.(split.(change.dims, (['-','×'],)))), change.time ./ master.time, group = change.type, xscale=:log10, ylabel="speed relative master", xlabel="first dimension length")
savefig(p, "diff.svg")

Project.toml

[deps]
CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"