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Library for validated numerics using interval arithmetic

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@v1.7) pkg> add IntervalArithmetic Updating registry at `~/.julia/registries/General.toml` Resolving package versions... Installed SetRounding ───────── v0.2.1 Installed FastRounding ──────── v0.3.1 Installed CRlibm_jll ────────── v1.0.1+0 Installed RoundingEmulator ──── v0.2.1 Installed ErrorfreeArithmetic ─...

The following conversion fails to return a valid interval: ```Julia julia> x = Float64(π) 3.141592653589793 julia> convert(Interval{BigFloat}, x).lo ≤ x ≤ convert(Interval{BigFloat}, x).hi false ``` The problem seems to stem...

bug

This is a follow-up of [this](https://discourse.julialang.org/t/redefining-functions-in-the-repl-alleviates-large-allocations-mwe-with-intervalarithmetic-jl/53515) discussion in discourse. Multiplication of intervals in functions defined inside a module leads to 6 extra allocations per `*`. Interestingly, redefining the function in...

IntervalArithmetic v0.20.6, Julia v1.8-rc1 ```julia julia> import IntervalArithmetic julia> rad2deg(IntervalArithmetic.Interval(1, 2)) ERROR: StackOverflowError: Stacktrace: [1] rad2deg(z::IntervalArithmetic.Interval{Float64}) (repeats 79984 times) @ Base.Math ./math.jl:334 ```

There recently have been [some discussions](https://discourse.julialang.org/t/discussion-on-why-i-no-longer-recommend-julia-by-yuri-vishnevsky/81151) about what can be done in Julia to prevent composing various package in a way that leads to silent error or nonsensical result. A...

As proposed in #528 by @lucaferranti . Unfortunately, it does not cover all the cases yet, like ``` julia julia> hull(1, 2, 3, 1..2) ERROR: StackOverflowError: ... julia> hull(1, 1)...

both on master and 1.0-dev ```julia julia> using IntervalArithmetic julia> interval(1, 2) + Inf [∞, ∞] ``` Not sure what it should return though, maybe `Interval(prevfloat(Inf), Inf)` ? 🤔

Supporting special functions would be nice (see e.g. https://github.com/JuliaIntervals/IntervalRootFinding.jl/issues/175). I thought already was an issue here about this, but I can't find it. This is only easy to do for...

enhancement

## What This PR fixes issues in 1.0-dev with decorated interval constructors. After this all related ITF tests pass. ## Changes ### Check for validity of interval Added inner constructor...

1.0-dev

This is a proposal for a better configuration mechanism for changing the directed rounding method (tight or accurate) and for choosing the type of powers (fast or tight). Usage: ```jl...