Division with ∞

Project.toml

@@ -1,7 +1,7 @@
 name = "Infinities"
 uuid = "e1ba4f0e-776d-440f-acd9-e1d2e9742647"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.1.12"
+version = "0.1.13"
 
 [compat]
 Aqua = "0.8"

src/Infinities.jl

@@ -1,9 +1,9 @@
 module Infinities
 
 import Base: angle, isone, iszero, isinf, isfinite, abs, one, oneunit, zero, isless, inv,
-                +, -, *, ==, <, ≤, >, ≥, fld, cld, div, mod, min, max, sign, signbit,
+                +, -, *, /, \, ==, <, ≤, >, ≥, fld, cld, div, mod, min, max, sign, signbit,
                 string, show, promote_rule, convert, getindex,
-                Bool, Integer
+                Bool, Integer, round, float, conj
 
 export ∞,  ℵ₀,  ℵ₁, RealInfinity, ComplexInfinity, InfiniteCardinal, NotANumber
 # The following is commented out for now to avoid conflicts with Infinity.jl
@@ -112,10 +112,13 @@ convert(::Type{ComplexInfinity{T}}, ::Infinity) where T = ComplexInfinity{T}()
 convert(::Type{ComplexInfinity}, ::Infinity) = ComplexInfinity()
 convert(::Type{ComplexInfinity{T}}, x::RealInfinity) where T = ComplexInfinity{T}(x)
 convert(::Type{ComplexInfinity}, x::RealInfinity) = ComplexInfinity(x)
+float(x::ComplexInfinity) = exp(im*angle(x)) * Inf
 
 
 sign(y::ComplexInfinity{<:Integer}) = mod(y.signbit,2) == 0 ? 1 : -1
-angle(x::ComplexInfinity) = π*x.signbit
+angle(x::ComplexInfinity) = π*mod(x.signbit, 2)
+conj(x::ComplexInfinity{Bool}) = x
+conj(x::ComplexInfinity) = ComplexInfinity(-x.signbit)
 
 show(io::IO, x::ComplexInfinity) = print(io, "exp($(x.signbit)*im*π)∞")
 

src/algebra.jl

@@ -57,6 +57,15 @@
 *(x::AllInfinities, y::AllInfinities) = _mul(x, y)
 *(x::InfiniteCardinal, y::InfiniteCardinal) = max(x, y)
 
+/(x::AllInfinities, y::Number) = x * inv(y)
+/(x::AllInfinities, y::Rational) = x * inv(y)
+/(x::AllInfinities, y::Complex) = x * inv(y)
+/(x::Number, y::AllInfinities) = x / float(y)
+/(x::Complex, y::AllInfinities) = x / float(y)
+/(x::Rational, y::Union{Infinity,InfiniteCardinal}) = zero(x)
+/(x::Rational, y::Union{RealInfinity,ComplexInfinity}) = x/ float(y)
+/(x::AllInfinities, y::AllInfinities) = x * inv(y)
+
 # just conventions somehow
 *(::Infinity, y::InfiniteCardinal) = y
 *(x::InfiniteCardinal, ::Infinity) = x
@@ -93,4 +102,7 @@ end
 # inv
 inv(::Union{Infinity,InfiniteCardinal}) = 0
 inv(x::RealInfinity) = inv(float(x))
-inv(x::ComplexInfinity) = zero(ComplexF64)
+inv(x::ComplexInfinity) = zero(ComplexF64)
+
+# round
+round(x::AllInfinities, mode::RoundingMode; kwds...) = round(float(x), mode; kwds...)

test/runtests.jl

@@ -205,6 +205,12 @@ using Aqua
         end
 
         @test Base.to_index(RealInfinity()) ≡ ℵ₀
+
+
+        @testset "round" begin
+            @test round(+∞, RoundNearest) ≡ Inf
+            @test round(-∞, RoundNearest) ≡ -Inf
+        end
     end
 
     @testset "ComplexInfinity" begin
@@ -288,6 +294,11 @@ using Aqua
 
         @test signbit(ComplexInfinity(3))
         @test !signbit(ComplexInfinity(100))
+
+        @test conj(exp(im)∞) ≡ exp(-im)∞
+        @test conj(ComplexInfinity(1)) == ComplexInfinity(1)
+        @test ComplexInfinity(1) == -∞
+        @test ComplexInfinity(-1) == -∞
     end
 
     @testset "Set" begin
@@ -324,6 +335,28 @@ using Aqua
         @test zero(-∞) ≡ zero(RealInfinity) ≡ 0.0
         @test zero(exp(0.1im)∞) ≡ zero(ComplexInfinity) ≡ 0.0+0.0im
     end
+
+    @testset "division" begin
+        @test (+∞) / 2.0 ≡ 2.0 \ (+∞) ≡ (+∞) / (2 //3) ≡ +∞
+        @test (+∞) / (1+im) ≡ (1+im) \ (+∞) ≡ exp(-im*π/4)*∞
+        @test (+∞) / (-2.0) ≡ (-2.0) \ (+∞) ≡ -∞
+        @test (-∞) / 2.0 ≡ (2.0) \ (-∞) ≡ -∞
+        @test (-∞) / (-2.0) ≡ (-2.0) \ (-∞) ≡ +∞
+
+        @test +∞ / 0 ≡ +∞ / 0.0 ≡ -∞ / (-0.0) ≡ +∞
+        @test -∞ / 0 ≡ -∞ / 0.0  ≡ +∞ / (-0.0) ≡ -∞ 
+
+        @test 2 / (+∞) ≡ 2.0 / (+∞) ≡ -2.0 / (-∞) ≡ 0.0
+        @test 2 / (-∞) ≡ 2.0 / (-∞) ≡ -2.0 / (+∞) ≡ -0.0
+        @test (1+im) / (+∞) ≡ (+∞) \ (1+im) ≡ 0.0+0.0im
+        @test (1+im) / (exp(im)∞) ≡ (1+im) / (exp(im)Inf) ≡ 0.0-0.0im
+        @test (exp(im)∞) \ (1+im) ≡ (exp(im)Inf) \ (1+im) ≡ 0.0+0.0im
+        @test (2//3) / ∞ ≡ 0 // 1
+        @test (2//3) / (+∞) ≡ 0.0
+        @test (2//3) / (exp(im*π/4)∞) ≡ 0.0 - 0.0im
+
+        @test_throws ArgumentError +∞ / +∞
+    end
 end