Integer(::RealInfinity) and Integer(::ComplexInfinity)

Project.toml

@@ -1,7 +1,7 @@
 name = "Infinities"
 uuid = "e1ba4f0e-776d-440f-acd9-e1d2e9742647"
 authors = ["Sheehan Olver <solver@mac.com>"]
-version = "0.0.2"
+version = "0.1.0"
 
 [compat]
 julia = "1"

src/Infinities.jl

@@ -2,7 +2,7 @@ module Infinities
 
 import Base: angle, isone, iszero, isinf, isfinite, abs, one, zero, isless, 
                 +, -, *, ==, <, ≤, >, ≥, fld, cld, div, mod, min, max, sign, signbit, 
-                string, show, promote_rule, convert
+                string, show, promote_rule, convert, getindex
 
 export ∞,  ℵ₀,  ℵ₁, RealInfinity, ComplexInfinity, InfiniteCardinal, NotANumber
 # The following is commented out for now to avoid conflicts with Infinity.jl

src/cardinality.jl

@@ -34,6 +34,14 @@ isinf(::InfiniteCardinal) = true
 isfinite(::InfiniteCardinal) = false
 
 Integer(::Infinity) = InfiniteCardinal{0}()
+function Integer(x::RealInfinity)
+    signbit(x) && throw(InexactError(:Integer, Integer, x))
+    ℵ₀
+end
+function Integer(x::ComplexInfinity)
+    iszero(angle(x)) || throw(InexactError(:Integer, Integer, x))
+    ℵ₀
+end
 
 ==(::InfiniteCardinal{N}, ::InfiniteCardinal{N}) where N = true
 ==(::InfiniteCardinal, ::InfiniteCardinal)= false
@@ -187,4 +195,17 @@ Base.Checked.checked_mul(::InfiniteCardinal{0}, x::Integer) = sign(x)*∞
 ##
 
 Base.hash(::InfiniteCardinal{0}) = 0x775431eef01bca90 # made up
-Base.hash(::InfiniteCardinal{1}) = 0x55437c69b794f8ce # made up
+Base.hash(::InfiniteCardinal{1}) = 0x55437c69b794f8ce # made up
+
+
+# avoid stack overflow
+getindex(A::Array, i1::InfiniteCardinal{0}, I::Integer...) = throw(BoundsError(A, i1, I...))
+
+Base._unsafe_getindex(::IndexStyle, A::AbstractArray, I::InfiniteCardinal{0}) = error("Overload getindex(::$(typeof(A)), ::InfiniteCardinal{0})")
+
+# Avoid too-strict restrictions in SubArray
+function getindex(V::SubArray{T,N}, I::Vararg{InfiniteCardinal{0},N}) where {T,N}
+  @boundscheck checkbounds(V, I...)
+  @inbounds r = V.parent[Base.reindex(V.indices, I)...]
+  r
+end

test/test_cardinality.jl

@@ -11,6 +11,9 @@ using Infinities, Base64, Base.Checked, Test
         @test zero(ℵ₀) ≡ 0
         @test one(ℵ₀) ≡ 1
         @test isinf(ℵ₀) && !isfinite(ℵ₀)
+        @test Integer(RealInfinity()) ≡ Integer(ComplexInfinity()) ≡ ℵ₀
+        @test_throws InexactError Integer(-∞)
+        @test_throws InexactError Integer(exp(0.1im)*∞)
     end
 
     @testset "equality" begin
@@ -125,4 +128,10 @@ using Infinities, Base64, Base.Checked, Test
         @test checked_sub(5, ℵ₀) ≡ -∞
         @test checked_mul(-5, ℵ₀) ≡ checked_mul(ℵ₀, -5) ≡ -∞
     end
+
+    @testset "indexing" begin
+        @test_throws BoundsError randn(3)[ℵ₀]
+        @test_throws ErrorException Base._unsafe_getindex(IndexCartesian(),permutedims(1:3)',ℵ₀)
+        @test_throws BoundsError view(randn(3),1:2)[ℵ₀]
+    end
 end