Merge pull request #3110 from JuliaLang/sk/float-rational-cmp

transitive comparison of floats and rationals

base/rational.jl

@@ -93,11 +93,11 @@ typemin{T<:Integer}(::Type{Rational{T}}) = -one(T)//zero(T)
 typemax{T<:Integer}(::Type{Rational{T}}) = one(T)//zero(T)
 
 isinteger(x::Rational) = x.den == 1
-isfloat64(x::Rational) = abs(x.num) <= x.den*maxintfloat(Float64)
+isfloat64(x::Rational) = ispow2(x.den) & (abs(x.num) <= x.den*maxintfloat(Float64))
 
 hash(x::Rational) = isinteger(x) ? hash(x.num) :
                     isfloat64(x) ? hash(float64(x)) :
-                    bitmix(hash(x.num),hash(x.den))
+                    bitmix(hash(x.num), hash(x.den))
 
 -(x::Rational) = (-x.num) // x.den
 +(x::Rational, y::Rational) = (x.num*y.den + x.den*y.num) // (x.den*y.den)
@@ -111,13 +111,13 @@ hash(x::Rational) = isinteger(x) ? hash(x.num) :
 ==(x::Integer , y::Rational) = y == x
 
 # needed to avoid ambiguity between ==(x::Real, z::Complex) and ==(x::Rational, y::Number)
-==(z::Complex , x::Rational) = isreal(z) && real(z) == x
-==(x::Rational, z::Complex ) = isreal(z) && real(z) == x
+==(z::Complex , x::Rational) = isreal(z) & (real(z) == x)
+==(x::Rational, z::Complex ) = isreal(z) & (real(z) == x)
 
-==(x::Rational, y::Number  ) = x.num == x.den*y
-==(x::Number  , y::Rational) = y == x
-==(x::Rational, y::FloatingPoint) = x.den==0 ? oftype(y,x)==y : x.num == x.den*y
+==(x::FloatingPoint, q::Rational) = ispow2(q.den) & (x == q.num/q.den) & (x*q.den == q.num)
+==(q::Rational, x::FloatingPoint) = ispow2(q.den) & (x == q.num/q.den) & (x*q.den == q.num)
 
+# TODO: fix inequalities to be in line with equality check
 < (x::Rational, y::Rational) = x.den == y.den ? x.num < y.num : x.num*y.den < x.den*y.num
 < (x::Rational, y::Real    ) = x.num < x.den*y
 < (x::Real    , y::Rational) = x*y.den < y.num

test/numbers.jl

@@ -681,7 +681,7 @@ end
 
 for a = -5:5, b = -5:5
     if a == b == 0; continue; end
-    @test a//b == a/b
+    @test !ispow2(b) || a//b == a/b
     @test a//b == a//b
     @test a//b == convert(Rational,a/b)
     if b == 0
@@ -708,6 +708,19 @@ for a = -5:5, b = -5:5
     end
 end
 
+@test 0.5 == 1//2
+@test 0.1 != 1//10
+@test 0.1 == 3602879701896397//36028797018963968
+@test realmin() != 1//(BigInt(2)^1022+1)
+@test realmin() == 1//(BigInt(2)^1022)
+@test realmin() != 1//(BigInt(2)^1022-1)
+@test realmin()/2 != 1//(BigInt(2)^1023+1)
+@test realmin()/2 == 1//(BigInt(2)^1023)
+@test realmin()/2 != 1//(BigInt(2)^1023-1)
+@test nextfloat(0.0) != 1//(BigInt(2)^1074+1)
+@test nextfloat(0.0) == 1//(BigInt(2)^1074)
+@test nextfloat(0.0) != 1//(BigInt(2)^1074-1)
+
 @test sqrt(2) == 1.4142135623730951
 
 @test 1+1.5 == 2.5