(possibly) small bug in constructing very tiny intervals with ..

[lucaferranti]

I am trying to construct the interval [1.0000000000000001, 1.0000000000000002]. Note that the lower bound is parsed to the float 1.0 and the upper bound is the next float. If I create the interval with .., then the upper bound is converted to its previous float in this case.

julia> a =  1.0000000000000001
1.0

julia> b =  1.0000000000000002
1.0000000000000002

julia> i1 = a..b
[1, 1]

julia> diam(i1)
0.0

julia> i1.lo == i1.hi
true

julia> i2 = interval(a, b)
[1, 1.00001]

julia> diam(i2)
2.220446049250313e-16

julia> i2.lo == i2.hi
false

interval does not have this issue, so I think the problem is with .. calling rationalize somewhere under the hood. I haven't checked the details of rationalize source code, but I think to remember it uses some continued fractions expansions under the hood. I guess that floating point numbers which are only a few ulps away are converted to the same rational number.

[lucaferranti]

This is actually a test in the ITF1788 testsuite:

b-textToInterval "[1.0000000000000001, 1.0000000000000002]" = [1.0, 0x1.0000000000001p+0] signal PossiblyUndefinedOperation;