fix float/rational vs mathconst comparisons

base/constants.jl

@@ -21,6 +21,47 @@ end
 =={s}(::MathConst{s}, ::MathConst{s}) = true
 ==(::MathConst, ::MathConst) = false
 
+# MathConsts are irrational, so unequal to everything else
+==(x::MathConst, y::Real) = false
+==(x::Real, y::MathConst) = false
+
+# MathConst vs FloatingPoint
+<(x::MathConst, y::Float64) = Float64(x,RoundUp) <= y
+<(x::Float64, y::MathConst) = x <= Float64(y,RoundDown)
+<(x::MathConst, y::Float32) = Float32(x,RoundUp) <= y
+<(x::Float32, y::MathConst) = x <= Float32(y,RoundDown)
+<(x::MathConst, y::Float16) = Float32(x,RoundUp) <= y
+<(x::Float16, y::MathConst) = x <= Float32(y,RoundDown)
+<(x::MathConst, y::BigFloat) = with_bigfloat_precision(precision(y)+32) do
+    big(x) < y
+end
+<(x::BigFloat, y::MathConst) = with_bigfloat_precision(precision(x)+32) do
+    x < big(y)
+end
+
+<=(x::MathConst,y::FloatingPoint) = x < y
+<=(x::FloatingPoint,y::MathConst) = x < y
+
+# MathConst vs Rational
+stagedfunction <{T}(x::MathConst, y::Rational{T})
+    bx = big(x())
+    bx < 0 && T <: Unsigned && return true
+    rx = rationalize(T,bx,tol=0)
+    rx < bx ? :($rx < y) : :($rx <= y)
+end
+stagedfunction <{T}(x::Rational{T}, y::MathConst)
+    by = big(y())
+    by < 0 && T <: Unsigned && return false
+    ry = rationalize(T,by,tol=0)
+    ry < by ? :(x <= $ry) : :(x < $ry)
+end
+<(x::MathConst, y::Rational{BigInt}) = big(x) < y
+<(x::Rational{BigInt}, y::MathConst) = x < big(y)
+
+<=(x::MathConst,y::Rational) = x < y
+<=(x::Rational,y::MathConst) = x < y
+
+
 hash(x::MathConst, h::UInt) = hash(object_id(x), h)
 
 -(x::MathConst) = -float64(x)

test/numbers.jl

@@ -814,6 +814,29 @@ end
 @test !(1//3 == NaN)
 @test !(1//3 > NaN)
 
+@test Float64(pi,RoundDown) < pi
+@test Float64(pi,RoundUp) > pi
+@test !(Float64(pi,RoundDown) > pi)
+@test !(Float64(pi,RoundUp) < pi)
+@test Float64(pi,RoundDown) <= pi
+@test Float64(pi,RoundUp) >= pi
+@test Float64(pi,RoundDown) != pi
+@test Float64(pi,RoundUp) != pi
+
+@test Float32(pi,RoundDown) < pi
+@test Float32(pi,RoundUp) > pi
+@test !(Float32(pi,RoundDown) > pi)
+@test !(Float32(pi,RoundUp) < pi)
+
+@test prevfloat(big(pi)) < pi
+@test nextfloat(big(pi)) > pi
+@test !(prevfloat(big(pi)) > pi)
+@test !(nextfloat(big(pi)) < pi)
+
+@test 2646693125139304345//842468587426513207 < pi
+@test !(2646693125139304345//842468587426513207 > pi)
+@test 2646693125139304345//842468587426513207 != pi
+
 @test sqrt(2) == 1.4142135623730951
 
 @test 1+1.5 == 2.5