Problem with small values

[lbenet]

I just came across the following:

julia> using ValidatedNumerics

julia> const epsilon = 1.0e-20
1.0e-20

julia> @interval(epsilon)
Interval(0.0, 0.0)

julia> Interval(epsilon)
Interval(1.0e-20, 1.0e-20)

The problem seems to be in convert (after expanding the macro):

julia> convert(Interval{Float64},epsilon)
Interval(0.0, 0.0)

[lbenet]

The problem is related to the use of rationalize in the convert method (line 49 of src/conversion.jl:

julia> rationalize(epsilon)
0//1

[dpsanders]

Ouch. Do you have a suggestion as to how to solve this?
@interval("1e-20") works.

I do not want to go back to using a string representation for the conversion, since that is very slow.
Maybe we can check if the resulting interval contains the starting float.

[lbenet]

No suggestion yet...

[dpsanders]

I mean something like

julia> function make_interval(x)
       II = convert(Interval{Float64}, x)
       if !(x ∈ II)
              II = convert(Interval{Float64}, string(x))
       end
       end
make_interval (generic function with 1 method)

julia> make_interval(1e-20)
[9.99999e-21, 1.00001e-20]

[lbenet]

Using a small variation of your code, all but one test pass; the failing test is: x^(1//3) --> x^(1 / 3)

[dpsanders]

I don't understand why that test would fail.

[dpsanders]

Do you have a branch with this change?

[lbenet]

I've pushed it only until now, sorry; its called "Iss136".

[dpsanders]

Nice catch. The problem is here:

julia> convert(Interval{BigFloat}, 1/3)
Interval(3.333333333333332999999999999999999999999999999999999999999999999999999999999968e-01, 3.333333333333333000000000000000000000000000000000000000000000000000000000000012e-01)

julia> convert(Interval{BigFloat}, 1//3)
Interval(3.333333333333333333333333333333333333333333333333333333333333333333333333333305e-01, 3.333333333333333333333333333333333333333333333333333333333333333333333333333348e-01)

Clearly the first is wrong.

[dpsanders]

Not sure how to find a solution that works for 1/3 and for 1e-20, though. It's possible that for BigFloat we'll just have to use the conversion via a string?

[lbenet]

Not sure how to solve it. I'm still, playing, but I've been bouncing myself against a wall...

One possibility is leave it as it is, with a note in the documentation and the docstrings.

[lbenet]

I didn't notice it before, but there are more failing tests...

[lbenet]

Pushed a new commit; not sure why, but locally few tests related to IntervalBox are not passing (also in master); probably something related to FixedSizeArrays...

[lbenet]

... but not what was problematic before.

[dpsanders]

Fixed by #137