simpler transitive Float == Rational equality implementation [#3102].

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)
@@ -111,30 +111,11 @@ 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
-
-function ==(x::Float64, y::Rational)
-    a, b = y.num, y.den
-    ((x==0) & (a==0) | isinf(x) & (b==0) & (a==sign(x))) && return true
-    u = reinterpret(Uint64, x)
-    s = copysign(int(uint(!isdenormal(x))<<52 + u & 0x000fffffffffffff), x)
-    p = min(1074, 1075-int((u>>52) & 0x7ff))
-    za, zb, zs = trailing_zeros(a), trailing_zeros(b), trailing_zeros(s)
-    (za+p == zb+zs) & ((a>>>za) == (b>>>zb)*(s>>>zs)) # a*2^p == b*s
-end
-==(x::Rational, y::Float64) = y == x
-
-function ==(x::Float32, y::Rational)
-    a, b = y.num, y.den
-    ((x==0) & (a==0) | isinf(x) & (b==0) & (a==sign(x))) && return true
-    u = reinterpret(Uint32, x)
-    s = copysign(int(uint(!isdenormal(x))<<23 + u & 0x007fffff), x)
-    p = min(149, 150-int((u>>23) & 0xff))
-    za, zb, zs = trailing_zeros(a), trailing_zeros(b), trailing_zeros(s)
-    (za+p == zb+zs) & ((a>>>za) == (b>>>zb)*(s>>>zs)) # a*2^p == b*s
-end
-==(x::Rational, y::Float32) = y == x
+==(z::Complex , x::Rational) = isreal(z) & (real(z) == x)
+==(x::Rational, z::Complex ) = isreal(z) & (real(z) == x)
+
+==(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