Make it easier to extend lcm/gcd/gcdx to custom types

(cherry picked from commit 85eb20f)

Author: sostock

base/intfuncs.jl

@@ -82,13 +82,15 @@ end
 
 gcd(a::Union{Integer,Rational}) = a
 lcm(a::Union{Integer,Rational}) = a
-gcd(a::Union{Integer,Rational}, b::Union{Integer,Rational}) = gcd(promote(a,b)...)
-lcm(a::Union{Integer,Rational}, b::Union{Integer,Rational}) = lcm(promote(a,b)...)
-gcd(a::Union{Integer,Rational}, b::Union{Integer,Rational}...) = gcd(a, gcd(b...))
-lcm(a::Union{Integer,Rational}, b::Union{Integer,Rational}...) = lcm(a, lcm(b...))
+gcd(a::Real, b::Real) = gcd(promote(a,b)...)
+lcm(a::Real, b::Real) = lcm(promote(a,b)...)
+gcd(a::Real, b::Real, c::Real...) = gcd(a, gcd(b, c...))
+lcm(a::Real, b::Real, c::Real...) = lcm(a, lcm(b, c...))
+gcd(a::T, b::T) where T<:Real = throw(MethodError(gcd, (a,b)))
+lcm(a::T, b::T) where T<:Real = throw(MethodError(lcm, (a,b)))
 
-gcd(abc::AbstractArray{<:Union{Integer,Rational}}) = reduce(gcd, abc; init=zero(eltype(abc)))
-lcm(abc::AbstractArray{<:Union{Integer,Rational}}) = reduce(lcm, abc; init=one(eltype(abc)))
+gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc; init=zero(eltype(abc)))
+lcm(abc::AbstractArray{<:Real}) = reduce(lcm, abc; init=one(eltype(abc)))
 
 function gcd(abc::AbstractArray{<:Integer})
     a = zero(eltype(abc))
@@ -147,7 +149,8 @@ function gcdx(a::T, b::T) where T<:Integer
     end
     a < 0 ? (-a, -s0, -t0) : (a, s0, t0)
 end
-gcdx(a::Union{Integer,Rational}, b::Union{Integer,Rational}) = gcdx(promote(a,b)...)
+gcdx(a::Real, b::Real) = gcdx(promote(a,b)...)
+gcdx(a::T, b::T) where T<:Real = throw(MethodError(gcdx, (a,b)))
 
 # multiplicative inverse of n mod m, error if none
 

test/intfuncs.jl

@@ -68,6 +68,17 @@ end
     @test gcdx(5, -12) == (1, 5, 2)
     @test gcdx(-25, -4) == (1, -1, 6)
 end
+@testset "gcd/lcm/gcdx for custom types" begin
+    struct MyRational <: Real
+        val::Rational{Int}
+    end
+    Base.promote_rule(::Type{MyRational}, T::Type{<:Real}) = promote_type(Rational{Int}, T)
+    (T::Type{<:Real})(x::MyRational) = T(x.val)
+
+    @test gcd(MyRational(2//3), 3) == gcd(2//3, 3) == gcd(Real[MyRational(2//3), 3])
+    @test lcm(MyRational(2//3), 3) == lcm(2//3, 3) == lcm(Real[MyRational(2//3), 3])
+    @test gcdx(MyRational(2//3), 3) == gcdx(2//3, 3)
+end
 @testset "invmod" begin
     @test invmod(6, 31) === 26
     @test invmod(-1, 3) === 2