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Library for validated numerics using interval arithmetic

Results 131 IntervalArithmetic.jl issues
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```jl X = IntervalBox(-10..10, 3) julia> X[1:2] 2-element Vector{Interval{Float64}}: [-10, 10] [-10, 10] ```

By defining e.g. ```jl +(::DirectedRounding{:tight}, a, b) ``` for intervals `a` and `b`.

I don't expect this to be common, but I did just run into it. ```julia import NumberIntervals import IntervalArithmetic ``` ```julia julia> [NumberIntervals.NumberInterval(0, 1), IntervalArithmetic.Interval(0, 1)] ERROR: StackOverflowError: Stacktrace: [1]...

(originally from https://github.com/JuliaReach/ReachabilityAnalysis.jl/pull/373#issuecomment-733224612) From doing `?in` ```julia in(item, collection) -> Bool ∈(item, collection) -> Bool ∋(collection, item) -> Bool Determine whether an item is in the given collection, in the...

Since ForwardDiff now no longer requires types to be `

Currently it falls back to `sind(::Real)` defined in Base: ```julia julia> sind(interval(0, 0)) ERROR: rem not defined for IntervalArithmetic.Interval{Float64} ```

…(sinpi(0.5..0.5)) == 0. Fixes #412. Now all tests pass, but running for instance `cospi(@biginterval(0.5))` returns a StackOverflowError on my machine (Ubuntu 20.04, Julia 1.5.0). ```julia julia> cospi(@biginterval(0.5)) ERROR: StackOverflowError: Stacktrace:...

The one-line change is believed to solve Issue #410. If preferred, the one-liner can be made into a full `if ... end` block. Let me know!

It looks like `sinpi(x)`, where `x` is an interval, is defined internally as `sin(x*\pi)`. Unfortunately this yields intervals that could be tightened; for instance: ``` julia> sinpi(1..1) [-3.21625e-16, 1.22465e-16] ```...