Overload inv, one, oneunit, zero and remove type-piracy (#61)

* Overload Base.literal_pow

* Add inv and tests

* remove inferrence test

* Fix ambiguity, add tests

* Support 3-tensors too

* Update test_cardinality.jl

* v0.1.10

Author: dlfivefifty

Project.toml

@@ -1,7 +1,7 @@
 name = "Infinities"
 uuid = "e1ba4f0e-776d-440f-acd9-e1d2e9742647"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.1.9"
+version = "0.1.10"
 
 [compat]
 Aqua = "0.8"

src/Infinities.jl

@@ -1,6 +1,6 @@
 module Infinities
 
-import Base: angle, isone, iszero, isinf, isfinite, abs, one, oneunit, zero, isless,
+import Base: angle, isone, iszero, isinf, isfinite, abs, one, oneunit, zero, isless, inv,
                 +, -, *, ==, <, ≤, >, ≥, fld, cld, div, mod, min, max, sign, signbit,
                 string, show, promote_rule, convert, getindex
 
@@ -42,6 +42,7 @@ one(::Type{Infinity}) = 1
 oneunit(::Type{Infinity}) = 1
 oneunit(::Infinity) = 1
 zero(::Infinity) = 0
+zero(::Type{Infinity}) = 0
 
 struct RealInfinity <: Real
     signbit::Bool
@@ -70,6 +71,13 @@ show(io::IO, y::RealInfinity) = print(io, string(y))
 
 Base.to_index(i::RealInfinity) = convert(Integer, i)
 
+one(::Type{RealInfinity}) = 1.0
+oneunit(::Type{RealInfinity}) = 1.0
+oneunit(::RealInfinity) = 1.0
+zero(::RealInfinity) = 0.0
+zero(::Type{RealInfinity}) = 0.0
+
+
 #######
 # ComplexInfinity
 #######
@@ -110,6 +118,12 @@ angle(x::ComplexInfinity) = π*x.signbit
 
 show(io::IO, x::ComplexInfinity) = print(io, "exp($(x.signbit)*im*π)∞")
 
+one(::Type{<:ComplexInfinity}) = one(ComplexF64)
+oneunit(::Type{<:ComplexInfinity}) = oneunit(ComplexF64)
+oneunit(::ComplexInfinity) = oneunit(ComplexF64)
+zero(::ComplexInfinity) = zero(ComplexF64)
+zero(::Type{<:ComplexInfinity}) = zero(ComplexF64)
+
 Base.hash(::Infinity) = 0x020113134b21797f # made up
 
 

src/algebra.jl

@@ -86,4 +86,11 @@ for OP in (:fld,:cld,:div)
         $OP(x::IntegerInfinities, y::Real) = _inffcd(x, y)
         $OP(::IntegerInfinities, ::IntegerInfinities) = NotANumber()
     end
-end
+end
+
+# Base.literal_pow
+
+# inv
+inv(::Union{Infinity,InfiniteCardinal}) = 0
+inv(x::RealInfinity) = inv(float(x))
+inv(x::ComplexInfinity) = zero(ComplexF64)

src/cardinality.jl

@@ -43,7 +43,15 @@ end
 
 Base.to_index(::Union{Infinity,InfiniteCardinal{0}}) = ℵ₀
 Base.to_shape(::Union{Infinity,InfiniteCardinal{0}}) = ℵ₀
-Base.to_shape(dims::Tuple{Vararg{Union{Infinity, Integer, AbstractUnitRange}}}) = map(Base.to_shape, dims)
+
+# only vectors, matrices, 3-tensors are supported
+Base.to_shape(dims::Tuple{Infinity, Vararg{Union{Integer, AbstractUnitRange}}}) = map(Base.to_shape, dims)
+Base.to_shape(dims::Tuple{Infinity, Infinity, Vararg{Union{Integer, AbstractUnitRange}}}) = map(Base.to_shape, dims)
+Base.to_shape(dims::Tuple{Union{Integer, AbstractUnitRange}, Infinity, Vararg{Union{Integer, AbstractUnitRange}}}) = map(Base.to_shape, dims)
+Base.to_shape(dims::Tuple{Infinity, Infinity, Infinity, Vararg{Union{Integer, AbstractUnitRange}}}) = map(Base.to_shape, dims)
+Base.to_shape(dims::Tuple{Infinity, Union{Integer, AbstractUnitRange}, Infinity, Vararg{Union{Integer, AbstractUnitRange}}}) = map(Base.to_shape, dims)
+Base.to_shape(dims::Tuple{Union{Integer, AbstractUnitRange}, Infinity, Infinity, Vararg{Union{Integer, AbstractUnitRange}}}) = map(Base.to_shape, dims)
+Base.to_shape(dims::Tuple{Union{Integer, AbstractUnitRange}, Union{Integer, AbstractUnitRange}, Infinity, Vararg{Union{Integer, AbstractUnitRange}}}) = map(Base.to_shape, dims)
 
 
 ##

test/runtests.jl

@@ -296,12 +296,41 @@ using Aqua
         @test ∞ in s
         @test 2 ∉ s
     end
+
+    @testset "Base.literal_pow" begin
+        @test Base.literal_pow(^, ℵ₀, Val(0)) ≡ ℵ₀^0 ≡ 1
+        @test Base.literal_pow(^, ℵ₀, Val(1)) ≡ ℵ₀^1 ≡ ℵ₀
+        @test Base.literal_pow(^, ℵ₀, Val(-1)) ≡ ℵ₀^(-1) ≡ 0
+
+        @test Base.literal_pow(^, ∞, Val(0)) ≡ ∞^0 ≡ 1
+        @test Base.literal_pow(^, ∞, Val(1)) ≡ ∞^1 ≡ ∞
+        @test Base.literal_pow(^, ∞, Val(-1)) ≡ ∞^(-1) ≡ 0
+
+        @test Base.literal_pow(^, -∞, Val(0)) ≡ (-∞)^0 ≡ 1.0
+        @test Base.literal_pow(^, -∞, Val(1)) ≡ (-∞)^1 ≡ -∞
+        @test Base.literal_pow(^, -∞, Val(-1)) ≡ (-∞)^(-1) ≡ 0.0
+
+        @test Base.literal_pow(^, ComplexInfinity(0.1), Val(0)) ≡ ComplexInfinity(0.1)^0 ≡ 1.0+0.0im
+        @test Base.literal_pow(^, ComplexInfinity(0.1), Val(1)) ≡ (ComplexInfinity(0.1))^1 ≡ ComplexInfinity(0.1)
+        @test Base.literal_pow(^, ComplexInfinity(0.1), Val(-1)) ≡ (ComplexInfinity(0.1))^(-1) ≡ 0.0+0.0im
+    end
+
+    @testset "one/zero/oneunit" begin
+        @test one(ℵ₀) ≡ one(∞)≡ one(ℵ₀) ≡ oneunit(∞) ≡ one(Infinity) ≡ one(InfiniteCardinal{0}) ≡ oneunit(Infinity) ≡ oneunit(InfiniteCardinal{0})  ≡ 1
+        @test one(-∞) ≡ oneunit(-∞) ≡ one(RealInfinity) ≡ oneunit(RealInfinity) ≡ 1.0
+        @test one(exp(0.1im)∞) ≡ oneunit(exp(0.1im)∞) ≡ one(ComplexInfinity) ≡ oneunit(ComplexInfinity) ≡ 1.0+0.0im
+
+        @test zero(ℵ₀) ≡ zero(∞) ≡ zero(Infinity) ≡ zero(InfiniteCardinal{0}) ≡ 0
+        @test zero(-∞) ≡ zero(RealInfinity) ≡ 0.0
+        @test zero(exp(0.1im)∞) ≡ zero(ComplexInfinity) ≡ 0.0+0.0im
+    end
 end
 
 
+
 include("test_cardinality.jl")
 include("test_ambiguity.jl")
 
 @testset "Project quality" begin
-    Aqua.test_all(Infinities, piracies=(; broken=true))
+    Aqua.test_all(Infinities)
 end

test/test_cardinality.jl

@@ -161,6 +161,15 @@ using Infinities, Base64, Base.Checked, Test
     @test string(ℵ₁) == stringmime("text/plain", ℵ₁) == "ℵ₁"
     @test Base.to_index(ℵ₀) ≡ Base.to_shape(ℵ₀) ≡ ℵ₀
     @test Base.to_shape((∞,)) ≡ (ℵ₀,)
+    @test Base.to_shape((∞,∞)) ≡ (ℵ₀,ℵ₀)
+    @test Base.to_shape((∞,1)) ≡ (ℵ₀,1)
+    @test Base.to_shape((1,∞)) ≡ (1,ℵ₀)
+    @test Base.to_shape((∞,∞,∞)) ≡ (ℵ₀,ℵ₀,ℵ₀)
+    @test Base.to_shape((∞,1,∞)) ≡ (ℵ₀,1,ℵ₀)
+    @test Base.to_shape((∞,∞,1)) ≡ (ℵ₀,ℵ₀,1)
+    @test Base.to_shape((1,∞,∞)) ≡ (1,ℵ₀,ℵ₀)
+    @test Base.to_shape((1,1,∞)) ≡ (1,1,ℵ₀)
+
 
     @testset "Set" begin
         s = Set([ℵ₀,ℵ₁,∞,1])