Add ThickNumbers extension

Project.toml

@@ -21,6 +21,7 @@ IrrationalConstants = "92d709cd-6900-40b7-9082-c6be49f344b6"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+ThickNumbers = "b57aa878-5b76-4266-befc-f8e007760995"
 
 [extensions]
 IntervalArithmeticArblibExt = "Arblib"
@@ -31,6 +32,7 @@ IntervalArithmeticIrrationalConstantsExt = "IrrationalConstants"
 IntervalArithmeticLinearAlgebraExt = "LinearAlgebra"
 IntervalArithmeticRecipesBaseExt = "RecipesBase"
 IntervalArithmeticSparseArraysExt = "SparseArrays"
+IntervalArithmeticThickNumbersExt = "ThickNumbers"
 
 [compat]
 Arblib = "1.3.0"
@@ -48,4 +50,5 @@ Random = "1.10"
 RecipesBase = "1"
 RoundingEmulator = "0.2"
 SparseArrays = "1.10"
+ThickNumbers = "1.1"
 julia = "1.10"

ext/IntervalArithmeticThickNumbersExt.jl

@@ -0,0 +1,100 @@
+module IntervalArithmeticThickNumbersExt
+
+import ThickNumbers as TN
+import IntervalArithmetic as IA
+
+# `IA.Interval <: Real`, so it cannot subtype `TN.ThickNumber`; it opts into the
+# ThickNumbers interface via the `isthick` trait instead.
+TN.isthick(::Type{<:IA.Interval}) = true
+
+# Required interface
+
+TN.loval(x::IA.Interval) = IA.inf(x)
+TN.hival(x::IA.Interval) = IA.sup(x)
+
+TN.lohi(::Type{IA.Interval{T}}, lo, hi) where {T} = IA.interval(T, lo, hi)
+TN.lohi(::Type{IA.Interval}, lo, hi) = IA.interval(lo, hi)
+
+TN.basetype(::Type{<:IA.Interval}) = IA.Interval
+TN.basetype(x::IA.Interval) = IA.Interval
+
+TN.valuetype(::Type{IA.Interval{T}}) where {T} = T
+TN.valuetype(x::IA.Interval{T}) where {T} = T
+
+# Optional interface
+
+TN.midrad(::Type{IA.Interval{T}}, m, r) where {T} = IA.interval(T, m, r; format = :midpoint)
+TN.midrad(::Type{IA.Interval}, m, r) = IA.interval(m, r; format = :midpoint)
+
+# `IA.emptyinterval` is used directly rather than the `ThickNumbers.emptyset`
+# default (`lohi(TN, typemax(T), typemin(T))`), which would round-trip through
+# `interval` and emit its "ill-formed interval" warning.
+TN.emptyset(::Type{IA.Interval{T}}) where {T} = IA.emptyinterval(IA.Interval{T})
+TN.emptyset(::Type{IA.Interval}) = IA.emptyinterval()
+TN.emptyset(x::IA.Interval) = IA.emptyinterval(x)
+
+TN.isempty_tn(x::IA.Interval) = IA.isempty_interval(x)
+
+TN.mid(x::IA.Interval) = IA.mid(x)
+TN.wid(x::IA.Interval) = IA.diam(x)
+TN.rad(x::IA.Interval) = IA.radius(x)
+TN.mag(x::IA.Interval) = IA.mag(x)
+TN.mig(x::IA.Interval) = IA.mig(x)
+
+TN.hull(a::IA.Interval, b::IA.Interval) = IA.hull(a, b)
+TN.hull(a::IA.Interval, b::IA.Interval, c::IA.Interval...) = IA.hull(a, b, c...)
+
+TN.isfinite_tn(x::IA.Interval) = IA.isbounded(x)
+TN.isinf_tn(x::IA.Interval) = IA.isunbounded(x)
+TN.isnan_tn(x::IA.Interval) = IA.isnai(x)
+
+TN.isequal_tn(a::IA.Interval, b::IA.Interval) = IA.isequal_interval(a, b)
+
+TN.issubset_tn(a::IA.Interval, b::IA.Interval) = IA.issubset_interval(a, b)
+# `IA.isstrictsubset` is defined as `issubset_interval(x,y) & !isequal_interval(x,y)`,
+# which is exactly ThickNumbers' loval/hival-based definition of a strict subset;
+# it is unrelated to `IA.isinterior`, which is a topological (open-set) notion and
+# uses `<` instead of `<=` at the endpoints (so, e.g., `interior([1,2],[1,3])` is
+# false while `is_strict_subset_tn([1,2],[1,3])` is true).
+TN.is_strict_subset_tn(a::IA.Interval, b::IA.Interval) = IA.isstrictsubset(a, b)
+TN.issupset_tn(a::IA.Interval, b::IA.Interval) = IA.issubset_interval(b, a)
+TN.is_strict_supset_tn(a::IA.Interval, b::IA.Interval) = IA.isstrictsubset(b, a)
+
+# `ThickNumbers` derives `Base.in(x::Real, a::ThickNumber)` from `loval`/`hival` for every
+# `ThickNumber` subtype, but a type that opts in via `isthick` (like `IA.Interval`) does not
+# inherit that dispatch and must define it directly. Unlike `IA.Interval == IA.Interval` or
+# `in_interval(::Interval, ::Interval)`, a real point's membership in an interval is always
+# decidable, and `IA.in_interval` already computes exactly that (`Base.in(::Interval,
+# ::Interval)` is the one IA purposely leaves unsupported, for `issubset_interval` instead).
+Base.in(x::Real, a::IA.Interval) = IA.in_interval(x, a)
+
+# `IA.strictprecedes` treats an empty interval as preceding (and being preceded
+# by) everything, and NaI as never satisfying either; `isless_tn` has neither
+# special case, so it is implemented directly from `inf`/`sup` rather than
+# reused from `strictprecedes`.
+TN.isless_tn(a::IA.Interval, b::IA.Interval) = isless(IA.sup(a), IA.inf(b))
+
+# `≺`, `≻`, `⪯` and `⪰` are functions distinct from `isless_tn` (not aliases of
+# it), each requiring its own method.
+TN.:(≺)(a::IA.Interval, b::IA.Interval) = IA.sup(a) < IA.inf(b)
+TN.:(≻)(a::IA.Interval, b::IA.Interval) = IA.inf(a) > IA.sup(b)
+TN.:(⪯)(a::IA.Interval, b::IA.Interval) = IA.sup(a) <= IA.inf(b)
+TN.:(⪰)(a::IA.Interval, b::IA.Interval) = IA.inf(a) >= IA.sup(b)
+
+TN.iseq_tn(a::IA.Interval, b::IA.Interval) =
+    (IA.isempty_interval(a) & IA.isempty_interval(b)) | ((IA.inf(a) == IA.inf(b)) & (IA.sup(a) == IA.sup(b)))
+
+function TN.isapprox_tn(
+    x::IA.Interval, y::IA.Interval;
+    atol::Real = 0,
+    rtol::Real = Base.rtoldefault(IA.numtype(x), IA.numtype(y), atol),
+    nans::Bool = false,
+)
+    (IA.isempty_interval(x) & IA.isempty_interval(y)) && return true
+    return TN.isequal_tn(x, y) ||
+        (IA.isbounded(x) && IA.isbounded(y) &&
+            max(abs(IA.sup(x) - IA.sup(y)), abs(IA.inf(x) - IA.inf(y))) <= max(atol, rtol * max(IA.mag(x), IA.mag(y)))) ||
+        (nans && IA.isnai(x) && IA.isnai(y))
+end
+
+end # module

test/interval_tests/IntervalArithmeticThickNumbersExt.jl

@@ -0,0 +1,234 @@
+@testset "IntervalArithmeticThickNumbersExt" begin
+    # ThickNumbers.jl is not yet registered in the General registry, so it cannot be
+    # listed as an ordinary test dependency in test/Project.toml without breaking
+    # `Pkg.instantiate` for everyone else. Run this testset only when ThickNumbers is
+    # already present in the active environment (e.g. added there with `Pkg.develop`).
+    if Base.find_package("ThickNumbers") === nothing
+        @info "ThickNumbers.jl is not available in this environment; skipping IntervalArithmeticThickNumbersExt tests. Pkg.develop it locally to run them (it is not yet registered in General)."
+    else
+        import ThickNumbers as TN
+        import ThickNumbers: ≺, ≻, ⪯, ⪰, ⫃, ⪽, ⫄, ⪾, ≐, ⩪
+
+        @testset "isthick trait" begin
+            @test TN.isthick(Interval)
+            @test TN.isthick(Interval{Float64})
+            @test TN.isthick(interval(1, 2))
+        end
+
+        @testset "lohi / loval / hival round trip" begin
+            x = TN.lohi(Interval{Float64}, 1 / 3, nextfloat(2 / 3))
+            @test x isa Interval{Float64}
+            @test TN.loval(x) == inf(x)
+            @test TN.hival(x) == sup(x)
+            @test in_interval(1 / 3, x)
+            @test in_interval(nextfloat(2 / 3), x)
+            @test TN.loval(x) ≈ 1 / 3
+            @test TN.hival(x) ≈ nextfloat(2 / 3)
+
+            y = TN.lohi(Interval, 1, 2)
+            @test y isa Interval{Float64}
+            @test TN.loval(y) == 1.0
+            @test TN.hival(y) == 2.0
+
+            # invalid bounds: IA's validating constructor warns and returns NaI, it
+            # does not throw.
+            local bad
+            @test_logs (:warn,) begin
+                bad = TN.lohi(Interval{Float64}, 2.0, 1.0)
+            end
+            @test isnai(bad)
+        end
+
+        @testset "midrad / mid / rad round trip" begin
+            x = TN.midrad(Interval{Float64}, 1 / 2, 1 / 6)
+            @test x isa Interval{Float64}
+            @test in_interval(1 / 2, x)
+            @test 1 / 6 <= TN.rad(x)
+            @test TN.rad(x) ≈ 1 / 6
+            @test TN.mid(x) ≈ 1 / 2
+
+            y = TN.midrad(Interval, 1.0, 2.0)
+            @test y isa Interval{Float64}
+            @test TN.valuetype(y) === Float64
+
+            # IA's midpoint-format `interval` constructor throws `DomainError` for a
+            # negative radius, rather than silently producing an empty interval (the
+            # behavior of ThickNumbers' generic `midrad` fallback).
+            @test_throws DomainError TN.midrad(Interval{Float64}, 1.0, -1.0)
+        end
+
+        @testset "basetype / valuetype" begin
+            @test TN.basetype(Interval) === Interval
+            @test TN.basetype(Interval{Float64}) === Interval
+            @test TN.basetype(interval(1, 2)) === Interval
+            @test TN.valuetype(Interval{Float64}) === Float64
+            @test TN.valuetype(interval(1, 2)) === Float64
+            @test TN.valuetype(interval(BigFloat, 1, 2)) === BigFloat
+        end
+
+        @testset "emptyset / isempty_tn" begin
+            e1 = TN.emptyset(Interval{Float64})
+            e2 = TN.emptyset(Interval)
+            e3 = TN.emptyset(interval(1.0, 2.0))
+            @test isequal_interval(e1, emptyinterval(Float64))
+            @test isequal_interval(e2, emptyinterval(Float64))
+            @test isequal_interval(e3, emptyinterval(Float64))
+            @test TN.isempty_tn(e1)
+            @test !TN.isempty_tn(interval(1.0, 2.0))
+            # NaI is not the empty set: `isempty_interval` (and hence `isempty_tn`)
+            # returns `false` for it, `isnan_tn` returns `true`.
+            @test !TN.isempty_tn(nai(Float64))
+        end
+
+        @testset "isnan_tn / isfinite_tn / isinf_tn" begin
+            @test TN.isnan_tn(nai(Float64))
+            @test !TN.isnan_tn(interval(1.0, 2.0))
+            @test TN.isfinite_tn(interval(1.0, 2.0))
+            @test !TN.isfinite_tn(interval(1.0, Inf))
+            @test TN.isinf_tn(entireinterval())
+            @test TN.isinf_tn(interval(1.0, Inf))
+            @test !TN.isinf_tn(interval(1.0, 2.0))
+            # NaI is neither finite nor infinite in this trait's sense.
+            @test !TN.isfinite_tn(nai(Float64))
+            @test !TN.isinf_tn(nai(Float64))
+        end
+
+        @testset "mid / wid / rad / mag / mig" begin
+            x = interval(1.0, 3.0)
+            @test TN.mid(x) == 2.0
+            @test TN.wid(x) == 2.0
+            @test TN.rad(x) == 1.0
+            @test TN.mag(x) == 3.0
+            @test TN.mig(x) == 1.0
+
+            y = interval(-2.0, 0.5) # straddles zero
+            @test TN.mig(y) == 0.0
+            @test TN.mag(y) == 2.0
+        end
+
+        @testset "hull" begin
+            x = interval(1.0, 3.0)
+            y = interval(-2.0, 0.5)
+            z = interval(10.0)
+            e = emptyinterval(Float64)
+
+            @test isequal_interval(TN.hull(x, y), interval(-2.0, 3.0))
+            @test isequal_interval(TN.hull(x, y, z), interval(-2.0, 10.0))
+
+            # `hull(emptyset, x) == x`, relying on `inf(emptyset) == +Inf` and
+            # `sup(emptyset) == -Inf`: downstream branch-and-bound code depends on
+            # this identity.
+            @test inf(e) == Inf
+            @test sup(e) == -Inf
+            @test isequal_interval(TN.hull(e, x), x)
+            @test isequal_interval(TN.hull(x, e), x)
+        end
+
+        @testset "subset / superset operators" begin
+            a = interval(1.0, 2.0)
+            b = interval(0.0, 3.0)
+            c = interval(1.0, 2.0) # == a
+            e = emptyinterval(Float64)
+
+            @test TN.issubset_tn(a, b)
+            @test !TN.issubset_tn(b, a)
+            @test TN.issubset_tn(e, a) # the empty set is a subset of everything
+            @test TN.issubset_tn(a, c) # subset includes equality
+
+            @test TN.is_strict_subset_tn(a, b)
+            @test !TN.is_strict_subset_tn(a, c) # equal, not strict
+
+            @test TN.issupset_tn(b, a)
+            @test !TN.issupset_tn(a, b)
+
+            @test TN.is_strict_supset_tn(b, a)
+            @test !TN.is_strict_supset_tn(c, a)
+
+            # unicode aliases are the same functions
+            @test (a ⫃ b) === TN.issubset_tn(a, b)
+            @test (a ⪽ b) === TN.is_strict_subset_tn(a, b)
+            @test (b ⫄ a) === TN.issupset_tn(b, a)
+            @test (b ⪾ a) === TN.is_strict_supset_tn(b, a)
+
+            # `is_strict_subset_tn` is loval/hival-based (matches IA's `isstrictsubset`),
+            # not a topological interior test: unlike `isinterior`, it does not
+            # require strict inequality at the shared endpoint.
+            p, q = interval(1.0, 2.0), interval(1.0, 3.0)
+            @test TN.is_strict_subset_tn(p, q)
+            @test !isinterior(p, q)
+        end
+
+        @testset "Base.in(::Real, ::Interval)" begin
+            # `ThickNumber` subtypes get this from ThickNumbers' generic
+            # `Base.in(x::Real, a::ThickNumber)`; `Interval` opts into the ThickNumbers
+            # interface via `isthick` rather than subtyping, so the extension defines it
+            # directly (`Base.in(::Interval, ::Interval)` remains purposely unsupported).
+            a = interval(1.0, 2.0)
+            @test 1.0 ∈ a && 1.5 ∈ a && 2.0 ∈ a
+            @test 0.99 ∉ a && 2.01 ∉ a
+            @test !(Inf ∈ a) && !(-Inf ∈ a)
+            @test_throws ArgumentError a ∈ a
+        end
+
+        @testset "Base.iszero(::Interval)" begin
+            # `iszero` asks whether the interval is the additive identity `[0, 0]`
+            # (`isthinzero`), which is decidable; it does not fall back to `==`,
+            # which throws for non-thin intervals.
+            @test iszero(interval(0.0, 0.0))
+            @test !iszero(interval(-1.0, 1.0)) # contains zero but is not [0, 0]
+            @test !iszero(interval(1.0, 2.0))
+            @test !iszero(emptyinterval(Float64))
+            @test !iszero(nai(Float64))
+        end
+
+        @testset "isless_tn, ≺, ≻, ⪯, ⪰" begin
+            a = interval(1.0, 2.0)
+            d = interval(5.0, 6.0)
+
+            @test TN.isless_tn(a, d)
+            @test !TN.isless_tn(d, a)
+            @test (a ≺ d) === true
+            @test (d ≺ a) === false
+            @test (d ≻ a) === true
+            @test (a ≻ d) === false
+            @test (a ⪯ d) === true
+            @test (d ⪰ a) === true
+
+            # touching endpoints: strict relations are false, non-strict are true
+            t = interval(2.0, 3.0)
+            @test !TN.isless_tn(a, t) # sup(a) == inf(t): not strictly less
+            @test (a ⪯ t) === true
+            @test !(a ≺ t)
+            @test (t ⪰ a) === true
+            @test !(t ≻ a)
+
+            # overlapping operands distinguish `x ≻ y` from `!(x ⪯ y)`: every
+            # relation must quantify over all member pairs, so neither order holds
+            o1, o2 = interval(2.0, 4.0), interval(1.0, 3.0)
+            @test !(o1 ≻ o2)
+            @test !(o2 ≺ o1)
+            @test !(o1 ⪰ o2)
+            @test !(o2 ⪯ o1)
+        end
+
+        @testset "isequal_tn, iseq_tn (≐), isapprox_tn (⩪)" begin
+            a = interval(1.0, 2.0)
+            c = interval(1.0, 2.0)
+            b = interval(1.0, 2.0 + eps(2.0))
+
+            @test TN.isequal_tn(a, c)
+            @test !TN.isequal_tn(a, b)
+            @test (a ≐ c) === true
+            @test (a ≐ b) === false
+
+            @test (a ⩪ interval(1.0 + 1e-10, 2.0 + 1e-10)) === true
+            @test !(a ⩪ interval(1.1, 2.1))
+            @test TN.isapprox_tn(a, a; atol = 0.0) === true
+
+            e1, e2 = emptyinterval(Float64), emptyinterval(Float64)
+            @test TN.isequal_tn(e1, e2)
+            @test (e1 ≐ e2) === true
+            @test (e1 ⩪ e2) === true
+        end
+    end
+end