Add specialized +, -, rem and mod for Rational and Integer (JuliaLang#35444)

Author: Liozou

base/rational.jl

@@ -263,6 +263,14 @@ for (op,chop) in ((:+,:checked_add), (:-,:checked_sub),
             xd, yd = divgcd(x.den, y.den)
             Rational(($chop)(checked_mul(x.num,yd), checked_mul(y.num,xd)), checked_mul(x.den,yd))
         end
+
+        function ($op)(x::Rational, y::Integer)
+            Rational(($chop)(x.num, checked_mul(x.den, y)), x.den)
+        end
+
+        function ($op)(y::Integer, x::Rational)
+            Rational(($chop)(checked_mul(x.den, y), x.num), x.den)
+        end
     end
 end
 
@@ -479,4 +487,3 @@ function gcdx(x::Rational, y::Rational)
     end
     c, a, b
 end
-

test/rational.jl

@@ -405,3 +405,22 @@ end
     @test gcd([5, 2, 1//2]) == 1//2
 end
 
+@testset "Binary operations with Integer" begin
+    @test 1//2 - 1 == -1//2
+    @test -1//2 + 1 == 1//2
+    @test 1 - 1//2 == 1//2
+    @test 1 + 1//2 == 3//2
+    for q in (19//3, -4//5), i in (6, -7)
+        @test rem(q, i) == q - i*div(q, i)
+        @test mod(q, i) == q - i*fld(q, i)
+    end
+
+    @test_throws OverflowError UInt(1)//2 - 1
+    @test_throws OverflowError 1 - UInt(5)//2
+    @test_throws OverflowError 1//typemax(Int64) + 1
+    @test_throws OverflowError Int8(1) + Int8(5)//(Int8(127)-Int8(1))
+
+    @test Int8(1) + Int8(4)//(Int8(127)-Int8(1)) == Int8(65) // Int8(63)
+    @test -Int32(1) // typemax(Int32) - Int32(1) == typemin(Int32) // typemax(Int32)
+    @test 1 // (typemax(Int128) + BigInt(1)) - 2 == (1 + BigInt(2)*typemin(Int128)) // (BigInt(1) + typemax(Int128))
+end