Support arithmetic with floats and InfiniteCardinal (#14)

* Support arithmetic with floats and InfiniteCardinal

* one(InfiniteCardinal)

* convert to float for RealInfinity, oneunit overrides

* increase coverage

Author: dlfivefifty

.github/workflows/ci.yml

@@ -12,7 +12,7 @@ jobs:
         version:
           - '1.0'
           - '1'
-          - '^1.6.0-0'
+          - '^1.7.0-0'
         os:
           - ubuntu-latest
           - macOS-latest

Project.toml

@@ -1,7 +1,7 @@
 name = "Infinities"
 uuid = "e1ba4f0e-776d-440f-acd9-e1d2e9742647"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.1.0"
+version = "0.1.1"
 
 [compat]
 julia = "1"

src/Infinities.jl

@@ -1,6 +1,6 @@
 module Infinities
 
-import Base: angle, isone, iszero, isinf, isfinite, abs, one, zero, isless, 
+import Base: angle, isone, iszero, isinf, isfinite, abs, one, oneunit, zero, isless, 
                 +, -, *, ==, <, ≤, >, ≥, fld, cld, div, mod, min, max, sign, signbit, 
                 string, show, promote_rule, convert, getindex
 
@@ -42,6 +42,8 @@ sign(y::Infinity) = 1
 angle(x::Infinity) = 0
 
 one(::Type{Infinity}) = 1
+oneunit(::Type{Infinity}) = 1
+oneunit(::Infinity) = 1
 zero(::Infinity) = 0
 
 isinf(::Infinity) = true
@@ -139,6 +141,16 @@ isfinite(::RealInfinity) = false
 promote_rule(::Type{Infinity}, ::Type{RealInfinity}) = RealInfinity
 convert(::Type{RealInfinity}, ::Infinity) = RealInfinity(false)
 
+convert(::Type{Float64}, x::RealInfinity) = sign(x)*Inf64
+convert(::Type{Float32}, x::RealInfinity) = sign(x)*Inf32
+convert(::Type{Float16}, x::RealInfinity) = sign(x)*Inf16
+Base.Float64(x::RealInfinity) = convert(Float64, x)
+Base.Float32(x::RealInfinity) = convert(Float32, x)
+Base.Float16(x::RealInfinity) = convert(Float16, x)
+Base.BigFloat(x::RealInfinity) = sign(x)*BigFloat(Inf)
+convert(::Type{AF}, x::RealInfinity) where AF<:AbstractFloat = sign(x)*convert(AF, Inf)
+
+
 signbit(y::RealInfinity) = y.signbit
 sign(y::RealInfinity) = 1-2signbit(y)
 angle(x::RealInfinity) = π*signbit(x)

src/cardinality.jl

@@ -28,7 +28,9 @@ sign(::InfiniteCardinal) = 1
 angle(::InfiniteCardinal) = 0
 abs(a::InfiniteCardinal) = a
 zero(::InfiniteCardinal) = 0
-one(::InfiniteCardinal) = 1
+one(::Type{<:InfiniteCardinal}) = 1
+oneunit(::Type{<:InfiniteCardinal}) = 1
+oneunit(::InfiniteCardinal) = 1
 
 isinf(::InfiniteCardinal) = true
 isfinite(::InfiniteCardinal) = false
@@ -153,11 +155,18 @@ end
 -(::InfiniteCardinal) = -∞
 -(x::Integer, ::InfiniteCardinal) = x - ∞
 
+for op in (:+, :-)
+    @eval begin
+        $op(x::Number, ::InfiniteCardinal) = $op(x, ∞)
+        $op(::InfiniteCardinal, x::Number) = $op(∞, x)
+    end
+end
+
 for OP in (:fld,:cld,:div)
-  @eval begin
-    $OP(x::InfiniteCardinal, ::Real) = x
-    $OP(::InfiniteCardinal, ::InfiniteCardinal) = NotANumber()
-  end
+    @eval begin
+        $OP(x::InfiniteCardinal, ::Real) = x
+        $OP(::InfiniteCardinal, ::InfiniteCardinal) = NotANumber()
+    end
 end
 
 div(::T, ::InfiniteCardinal) where T<:Real = zero(T)
@@ -205,7 +214,7 @@ Base._unsafe_getindex(::IndexStyle, A::AbstractArray, I::InfiniteCardinal{0}) =
 
 # Avoid too-strict restrictions in SubArray
 function getindex(V::SubArray{T,N}, i1::InfiniteCardinal{0}, I::Integer...) where {T,N}
-  @boundscheck checkbounds(V, i1, I...)
-  @inbounds r = V.parent[Base.reindex(V.indices, tuple(i1, I...))...]
-  r
+    @boundscheck checkbounds(V, i1, I...)
+    @inbounds r = V.parent[Base.reindex(V.indices, tuple(i1, I...))...]
+    r
 end

test/runtests.jl

@@ -35,7 +35,7 @@ import Infinities: Infinity
         @test ∞*∞ ≡ ∞
         @test ∞ - ∞ isa NotANumber
 
-        @test one(∞) ≡ 1
+        @test one(∞) ≡ one(Infinity) ≡ oneunit(∞) ≡ oneunit(Infinity) ≡ 1
         @test zero(∞) ≡ 0
 
         @test !isone(∞)
@@ -191,6 +191,13 @@ import Infinities: Infinity
             @test max(5, RealInfinity()) ≡ max(RealInfinity(), 5) ≡ RealInfinity()
             @test max(5, -∞) ≡ max(-∞, 5) ≡ 5
         end
+
+        @testset "convert" begin
+            @test convert(Float64, -∞) ≡ Float64(-∞) ≡ -Inf
+            @test convert(Float32, -∞) ≡ Float32(-∞) ≡ -Inf32
+            @test convert(Float16, -∞) ≡ Float16(-∞) ≡ -Inf16
+            @test convert(BigFloat, -∞)::BigFloat == BigFloat(-∞)::BigFloat == -BigFloat(Inf)
+        end
     end
 
     @testset "ComplexInfinity" begin

test/test_cardinality.jl

@@ -9,7 +9,7 @@ using Infinities, Base64, Base.Checked, Test
         @test Integer(∞) ≡ convert(Integer,∞) ≡ Integer(ℵ₀) ≡ convert(Integer, ℵ₀) ≡ ℵ₀
         @test abs(ℵ₀) ≡ ℵ₀
         @test zero(ℵ₀) ≡ 0
-        @test one(ℵ₀) ≡ 1
+        @test one(ℵ₀) ≡ one(InfiniteCardinal{0}) ≡ oneunit(ℵ₀) ≡ oneunit(InfiniteCardinal{0}) ≡ 1
         @test isinf(ℵ₀) && !isfinite(ℵ₀)
         @test Integer(RealInfinity()) ≡ Integer(ComplexInfinity()) ≡ ℵ₀
         @test_throws InexactError Integer(-∞)
@@ -94,6 +94,11 @@ using Infinities, Base64, Base.Checked, Test
         @test 5 * ℵ₀ ≡ ℵ₀ * 5 ≡ ℵ₀
         @test 5.0ℵ₀ ≡ ℵ₀*5.0 ≡ RealInfinity()
         @test_throws ArgumentError (-5) * ℵ₀
+
+        @test ℵ₀ - 5.1 ≡ ∞
+        @test ℵ₀ + 5.1 ≡ ∞
+        @test 5.1 + ℵ₀ ≡ ∞
+        @test 5.1 - ℵ₀ ≡ -∞
     end
 
     @testset "fld/cld/div/mod" begin