Fix //(x::Number, y::Complex)

Author: nhz2

base/rational.jl

@@ -105,10 +105,19 @@ function //(x::Rational, y::Rational)
 end
 
 //(x::Complex, y::Real) = complex(real(x)//y, imag(x)//y)
-//(x::Number, y::Complex) = x*conj(y)//abs2(y)
-
-function //(x::Union{Integer, Rational, Complex{<:Union{Rational, Integer}}}, y::Complex{<:Union{Rational, Integer}})
-    x/y
+function //(x::Number, y::Complex{<:Rational})
+    c, d = reim(y)
+    if (isinf(c) | isinf(d))
+        x * conj(zero(y))
+    else
+        x * conj(y)
+    end//abs2(y)
+end
+function //(x::Number, y::Complex{<:Integer})
+    c, d = reim(y)
+    c_r, d_r = divgcd(c, d)
+    abs2y_r = checked_add(checked_mul(c, c_r), checked_mul(d, d_r))
+    (x * complex(c_r, checked_neg(d_r)))//abs2y_r
 end
 function //(x::Integer, y::Complex{<:Integer})
     a, c, d = promote(x, reim(y)...)

test/rational.jl

@@ -215,6 +215,7 @@ end
     @test_throws DivideError (0//1) / complex(0, 0)
     @test_throws DivideError (1//1) / complex(0, 0)
     @test_throws DivideError (1//0) / complex(0, 0)
+    @test_throws DivideError complex(1//0) // complex(1//0, 1//0)
     @test_throws DivideError 1 // complex(0, 0)
     @test_throws DivideError 0 // complex(0, 0)
     @test_throws DivideError complex(1) // complex(0, 0)
@@ -250,6 +251,14 @@ end
             end
         end
     end
+    @testset "exact division by an infinite complex number" begin
+        for y ∈ (1 // 0, -1 // 0)
+            @test (7 // complex(y)) == 0
+            @test (Rational(7) // complex(y)) == 0
+            @test (complex(7) // complex(y)) == 0
+            @test (complex(Rational(7)) // complex(y)) == 0
+        end
+    end
 end
 
 # check type of constructed rationals
@@ -633,6 +642,10 @@ end
 # issue #16282
 @test_throws MethodError 3 // 4.5im
 
+# issue #60137
+@test_throws MethodError 3.0 // (1 + 0im)
+@test_throws MethodError 3.0 // (1//0 + 0im)
+
 # issue #31396
 @test round(1//2, RoundNearestTiesUp) === 1//1