overflow in Rational arithmetic

[JeffBezanson]

Rational - Int comparisons are susceptible to overflow:

julia> 3//2 > typemax(Int)
true

This is due to multiplying the integer argument by the rational's denominator.

Other operations that use * this way are similarly afflicted:

julia> r = (typemax(Int)-1)//typemax(Int)
9223372036854775806//9223372036854775807

julia> div(r,2)
-4611686018427387903

[quinnj]

Looks like we've made some progress on this:

julia> 3//2 > typemax(Int)
false

[Keno]

Given how easy it is to overflow Rational, maybe it would be a good idea to make rations use checked arithmetic?

[vtjnash]

Rationals need to be fixed 0.4 (what this? they even had their own tag), so I've picked a random issue and tagged it 0.4.

And yes, I'm volunteering myself if nobody else beats me too it.

[simonbyrne]

Note that comparisons are broken even without overflow:

julia> a = 1//3
1//3

julia> b = 1/3
0.3333333333333333

julia> BigFloat(a) > BigFloat(b)
true

julia> a > b
false

julia> a < b
false

julia> a == b
false

julia> a >= b
true

julia> a <= b
true

However I don't know of any great way to fix this. One idea would be to sequentially compare each element of the continued fraction expansion of each number (obtained via the Euclidean algorithm).

[simonbyrne]

These should now all be sorted: if not, please reopen.