Make iszero throw FPTNException; add iszero_tn

docs/src/developers.md

@@ -65,6 +65,6 @@ It must implement [`loval`](@ref), [`hival`](@ref), [`lohi`](@ref), [`basetype`]
 supported arithmetic, and any needed derived methods. These may include [`mid`](@ref),
 [`wid`](@ref), [`rad`](@ref), [`mag`](@ref), [`mig`](@ref), [`hull`](@ref),
 [`emptyset`](@ref), [`isempty_tn`](@ref), [`isnan_tn`](@ref), [`isinf_tn`](@ref),
-[`isfinite_tn`](@ref), and `iszero`.
+[`isfinite_tn`](@ref), and [`iszero_tn`](@ref).
 
 Use `isthick(x)` to recognize both kinds of implementation.

docs/src/index.md

@@ -33,6 +33,10 @@ returning `true` would imply that `x == y` *for any choice* `x ∈ X` and `y ∈
 unless `X` and `Y` are either empty or each contain only a single value. Concretely, if `1..3` constructs an interval, then `1..3 == 1..3` returning `true` would require that `1.5 == 1.5` and also `1.5 == 2.5` since both `1.5` and `2.5` can be drawn from `1..3`. This is obviously impossible,
 thus having `1..3 == 1..3` return `true` would be a violation of the FPTN; it must error instead.
 
+Unary predicates have the same constraint. If `X` contains both zero and nonzero values,
+`iszero(X)` cannot return one `Bool`. It therefore errors; [`iszero_tn`](@ref) instead
+reports whether `X` is the additive identity `[0, 0]`.
+
 Because numbers are iterable in Julia, set operations like `X ⊆ Y` also cannot be defined (it would require that each number in `X` is a subset of every number in `Y`); however, operations like `intersect(X, Y)` (i.e., `X ∩ Y`) are valid because `x ∩ y` returns `∅` if `x != y` and `∅` is a subset of all other sets.
 
 To avoid violating the FPTN, we replace operators like `==` with custom operators that work only on `ThickNumber{T}` but not `T`. For `Base` Julia functions, a convention is to add `_tn` after the standard function name: `isequal_tn(X, Y)` replaces the "intent" of `isequal(X, Y)`. Often these have unicode equivalents, which typically (though not always) involve a "dot" somewhere in the symbol.
@@ -60,6 +64,7 @@ You can also check a few basic properties, like whether the values contained in
 - [`isfinite_tn(X)`](@ref)
 - [`isinf_tn(X)`](@ref)
 - [`isnan_tn(X)`](@ref)
+- [`iszero_tn(X)`](@ref): whether `X` is the single point zero
 
 ### Type information
 

docs/src/user_api.md

@@ -32,6 +32,7 @@ wid
 isfinite_tn
 isinf_tn
 isnan_tn
+iszero_tn
 ```
 
 ## Comparison operators

ext/ThickNumbersForwardDiffExt.jl

@@ -45,10 +45,10 @@ ForwardDiff._div_partial(partial::Real, x::ThickNumber) = partial / x
 ForwardDiff._div_partial(partial::ThickNumber, x::Real) = partial / x
 ForwardDiff._div_partial(partial::ThickNumber, x::ThickNumber) = partial / x
 
-# ForwardDiff's `iszero_tuple` tests each partial with `==`, which ThickNumber
-# disables. Test exact-zeroness with `iszero` instead (defined for ThickNumber and,
-# recursively, for nested Duals over ThickNumbers).
-ForwardDiff.iszero_tuple(tup::NTuple{N,V}) where {N,V<:ThickLike} = all(iszero, tup)
+# ForwardDiff needs an unambiguous zero test for thick partials.
+ThickNumbers.iszero_tn(d::ThickDual) = iszero_tn(value(d)) & iszero_tn(partials(d))
+ThickNumbers.iszero_tn(p::Partials{N,V}) where {N,V<:ThickLike} = all(iszero_tn, p.values)
+ForwardDiff.iszero_tuple(tup::NTuple{N,V}) where {N,V<:ThickLike} = all(iszero_tn, tup)
 
 Base.promote_rule(::Type{TN}, ::Type{Dual{T,V,N}}) where {TN<:ThickNumber,T,V<:Number,N} = Dual{T, promote_dual(TN, V),N}
 

src/ThickNumbers.jl

@@ -22,7 +22,7 @@ export emptyset, hull, issubset_tn, ⫃, is_strict_subset_tn, ⪽, issupset_tn,
 export isequal_tn, iseq_tn, ≐, isapprox_tn, ⩪, isless_tn, ≺, ≻, ⪯, ⪰
 
 # Unary
-export isfinite_tn, isinf_tn, isnan_tn
+export isfinite_tn, isinf_tn, isnan_tn, iszero_tn
 
 # Types
 
@@ -320,10 +320,17 @@ mig(x::ThickNumber{T}) where T = zero(T) ∈ x ? zero(T) : min(abs(loval(x)), ab
 mag(x::Real) = abs(x)
 mig(x::Real) = abs(x)
 
-# A thick number is zero exactly when it is the degenerate set `[0, 0]`. Unlike
-# `==`, this is unambiguous, so it is defined (and needed by ForwardDiff, which
-# tests partials for exact zero).
-Base.iszero(x::ThickNumber) = iszero(loval(x)) & iszero(hival(x))
+"""
+    iszero_tn(x)
+
+Return `true` if both endpoints of `x` are zero, `false` otherwise.
+For point numbers, equivalent to `iszero(x)`.
+"""
+iszero_tn(x::ThickNumber) = iszero(loval(x)) & iszero(hival(x))
+
+iszero_tn(x::Number) = iszero(x)
+
+Base.iszero(::ThickNumber) = throw(FPTNException(iszero, iszero_tn))
 
 Base.promote_rule(::Type{ThickNumber{T}}, ::Type{ThickNumber{S}}) where {T<:Number,S<:Number} = ThickNumber{promote_type(T,S)}
 

test/runtests.jl

@@ -31,11 +31,13 @@ using MidRadArith
     @test mig(-3.0) === 3.0
     @test mag(2) === 2
     @test mig(2) === 2
-    # iszero: true only for the degenerate set [0, 0]
-    @test iszero(Interval(0, 0))
-    @test !iszero(Interval(0, 1))
-    @test !iszero(Interval(-1, 0))
-    @test !iszero(Interval(-1, 1))
+    # Only [0, 0] is the additive identity.
+    @test iszero_tn(Interval(0, 0))
+    @test !iszero_tn(Interval(0, 1))
+    @test !iszero_tn(Interval(-1, 0))
+    @test !iszero_tn(Interval(-1, 1))
+    @test iszero_tn(0.0) && !iszero_tn(1.0)
+    @test_throws FPTNException iszero(Interval(0, 0))
     @test lohi(Interval{Float64}, 1, 3) === x
     @test midrad(Interval{Float64}, 2, 1) === x
     @test basetype(Interval{Float64}) === Interval