David P. Sanders

Arithmetic with numbers of different types should be defined

3

```jl julia> X = 3..4 [3, 4] julia> @which X / 3.1 /(a::Interval{T}, x::T) where T @which X / Float32(3.1) /(x::Number, y::Number) in Base at promotion.jl:314 ``` The version with...

```jl IntervalBox{Float32}(X::IntervalBox) = IntervalBox(Interval{Float32}.(X)) ```

Currently in the `:accurate` directed rounding mode, we round the results of operations outward by adding or subtracting 1 ulp. However, different functions at different precisions may have different numbers...

Bugs with tiny numbers

34

```jl julia> tiny = interval(0, floatmin()) [0, 2.22508e-308] julia> huge = interval(floatmax(), Inf) [1.79769e+308, ∞] julia> tiny * tiny [0, 0] julia> huge * huge [1.79769e+308, ∞] julia> huge /...

Use IntervalSets.jl for set operations

2

cf. discussion in https://github.com/JuliaMath/IntervalSets.jl/pull/55 This is related to redefining `..` to *not* do clever tricks and just take floating-point endpoints at face value.

Float interval + BigFloat interval should be Float interval?

5

`x::Interval{Float64}` + `y::Interval{BigFloat}` should give `Interval{Float64}`?

Print intervals as `3..4`?

7

Maybe it would be less confusing to print out intervals as `3..4` instead of `[3, 4]`?

API for choosing power function

13

We need to decide on an API for how to specify whether powers will use the slow but accurate version (via MPFR) or the fast but less accurate version (via...