Make inv(::Complex) return zero when input has Inf magnitude (#32050)

Author: giordano

base/complex.jl

@@ -259,7 +259,11 @@ julia> conj(1 + 3im)
 conj(z::Complex) = Complex(real(z),-imag(z))
 abs(z::Complex)  = hypot(real(z), imag(z))
 abs2(z::Complex) = real(z)*real(z) + imag(z)*imag(z)
-inv(z::Complex)  = conj(z)/abs2(z)
+function inv(z::Complex)
+    c, d = reim(z)
+    (isinf(c) | isinf(d)) && return complex(copysign(zero(c), c), flipsign(-zero(d), d))
+    complex(c, -d)/(c * c + d * d)
+end
 inv(z::Complex{<:Integer}) = inv(float(z))
 
 +(z::Complex) = Complex(+real(z), +imag(z))
@@ -346,7 +350,7 @@ function /(a::Complex{T}, b::Complex{T}) where T<:Real
 end
 
 inv(z::Complex{<:Union{Float16,Float32}}) =
-    oftype(z, conj(widen(z))/abs2(widen(z)))
+    oftype(z, inv(widen(z)))
 
 /(z::Complex{T}, w::Complex{T}) where {T<:Union{Float16,Float32}} =
     oftype(z, widen(z)*inv(widen(w)))
@@ -430,6 +434,7 @@ end
 
 function inv(w::ComplexF64)
     c, d = reim(w)
+    (isinf(c) | isinf(d)) && return complex(copysign(0.0, c), flipsign(-0.0, d))
     half = 0.5
     two = 2.0
     cd = max(abs(c), abs(d))

test/complex.jl

@@ -999,6 +999,46 @@ end
     end
 end
 
+@testset "division by Inf, issue#23134" begin
+    @testset "$T" for T in (Float32, Float64, BigFloat)
+        @test isequal(one(T) / complex(T(Inf)),         complex(zero(T), -zero(T)))
+        @test isequal(one(T) / complex(T(Inf), one(T)), complex(zero(T), -zero(T)))
+        @test isequal(one(T) / complex(T(Inf), T(NaN)), complex(zero(T), -zero(T)))
+        @test isequal(one(T) / complex(T(Inf), T(Inf)), complex(zero(T), -zero(T)))
+
+        @test isequal(one(T) / complex(T(-Inf)),         complex(-zero(T), -zero(T)))
+        @test isequal(one(T) / complex(T(-Inf), one(T)), complex(-zero(T), -zero(T)))
+        @test isequal(one(T) / complex(T(-Inf), T(NaN)), complex(-zero(T), -zero(T)))
+        @test isequal(one(T) / complex(T(-Inf), T(Inf)), complex(-zero(T), -zero(T)))
+
+        @test isequal(one(T) / complex(T(Inf),-zero(T)), complex(zero(T), zero(T)))
+        @test isequal(one(T) / complex(T(Inf),-one(T)),  complex(zero(T), zero(T)))
+        @test isequal(one(T) / complex(T(Inf),T(-NaN)),  complex(zero(T), zero(T)))
+        @test isequal(one(T) / complex(T(Inf),T(-Inf)),  complex(zero(T), zero(T)))
+
+        @test isequal(one(T) / complex(T(-Inf),-zero(T)),complex(-zero(T), zero(T)))
+        @test isequal(one(T) / complex(T(-Inf),-one(T)), complex(-zero(T), zero(T)))
+        @test isequal(one(T) / complex(T(-Inf),T(-NaN)), complex(-zero(T), zero(T)))
+        @test isequal(one(T) / complex(T(-Inf),T(-Inf)), complex(-zero(T), zero(T)))
+
+        @test isequal(one(T) / complex(zero(T), T(Inf)), complex(zero(T), -zero(T)))
+        @test isequal(one(T) / complex(one(T),  T(Inf)), complex(zero(T), -zero(T)))
+        @test isequal(one(T) / complex(T(NaN),  T(Inf)), complex(zero(T), -zero(T)))
+
+        @test isequal(one(T) / complex(zero(T), T(-Inf)), complex(zero(T), zero(T)))
+        @test isequal(one(T) / complex(one(T),  T(-Inf)), complex(zero(T), zero(T)))
+        @test isequal(one(T) / complex(T(NaN),  T(-Inf)), complex(zero(T), zero(T)))
+
+        @test isequal(one(T) / complex(-zero(T), T(Inf)), complex(-zero(T), -zero(T)))
+        @test isequal(one(T) / complex(-one(T),  T(Inf)), complex(-zero(T), -zero(T)))
+        @test isequal(one(T) / complex(T(-NaN),  T(Inf)), complex(-zero(T), -zero(T)))
+
+        @test isequal(one(T) / complex(-zero(T), T(-Inf)), complex(-zero(T), zero(T)))
+        @test isequal(one(T) / complex(-one(T),  T(-Inf)), complex(-zero(T), zero(T)))
+        @test isequal(one(T) / complex(T(-NaN),  T(-Inf)), complex(-zero(T), zero(T)))
+    end
+end
+
 @testset "complex^real, issue #14342" begin
     for T in (Float32, Float64, BigFloat), p in (T(-21//10), -21//10)
         z = T(2)+0im