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This repository was archived by the owner on Nov 26, 2025. It is now read-only.
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`ValidatedNumerics.jl` is a Julia meta-package for performing *Validated Numerics* in Julia, i.e. *rigorous* computations with finite-precision floating-point arithmetic.
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All calculations are carried out using **interval arithmetic**: all quantities are treated as intervals, which are propagated throughout a calculation. The final result is an interval that is *guaranteed* to contain the correct result, starting from the given initial data.
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The aim of the package is correctness over speed, although performance considerations are also taken into account.
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### Authors
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-[Luis Benet](http://www.cicc.unam.mx/~benet/), Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México (UNAM)
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-[David P. Sanders](http://sistemas.fciencias.unam.mx/~dsanders), Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)
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### Contributors
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- Oliver Heimlich
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- Nikolay Kryukov
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- John Verzani
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`ValidatedNumerics.jl` is a suite of Julia packages for performing *Validated Numerics* in Julia, i.e. *rigorous* computations with finite-precision floating-point arithmetic, using **interval arithmetic**: quantities are treated as intervals that are propagated throughout a calculation. The final result is an interval that is *guaranteed* to contain the correct result, starting from the given initial data.
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The aims of the package are both correctness and good performance.
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## Installation
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julia> Pkg.add("ValidatedNumerics")
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```
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## Meta-package
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Since version 0.9, `ValidatedNumerics.jl` is a meta-package that automatically installs and reexports the following packages from the [`JuliaIntervals` GitHub organization](https://github.com/JuliaIntervals):
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Since version 0.9, `ValidatedNumerics.jl` is a meta-package that reexports the following packages from the [`JuliaIntervals` organization](https://github.com/JuliaIntervals) on GitHub:
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-[`IntervalArithmetic.jl`](https://github.com/JuliaIntervals/IntervalArithmetic.jl) -- fundamental arithmetic and elementary operations on intervals
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-[`IntervalArithmetic.jl`](https://github.com/JuliaIntervals/IntervalArithmetic.jl): arithmetic and elementary functions on intervals
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-[`IntervalRootFinding.jl`](https://github.com/JuliaIntervals/IntervalRootFinding.jl) -- find roots of functions in a guaranteed way
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-[`IntervalRootFinding.jl`](https://github.com/JuliaIntervals/IntervalRootFinding.jl): find roots of functions in a guaranteed way
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-[`IntervalConstraintProgramming.jl`](https://github.com/JuliaIntervals/IntervalConstraintProgramming.jl) -- characterization of feasible sets of inequalities
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-[`IntervalConstraintProgramming.jl`](https://github.com/JuliaIntervals/IntervalConstraintProgramming.jl): characterization of feasible sets of equations and inequalities
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## Standard for Interval Arithmetic: IEEE 1788-2015
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-[`IntervalContractors.jl`](https://github.com/JuliaIntervals/IntervalContractors.jl): contractors and reverse (or inverse) functions
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## Documentation
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Documentation is available separately for each of the above packages.
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## IEEE Standard 1788-2015 - IEEE Standard for Interval Arithmetic
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The IEEE Std 1788-2015 - IEEE Standard for Interval Arithmetic was [published](https://standards.ieee.org/findstds/standard/1788-2015.html) in June 2015. We are working towards having `ValidatedNumerics` be conformant with this standard.
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To do so, we have incorporated tests from the excellent [ITF1788 test suite](https://github.com/oheim/ITF1788), originally written by Marco Nehmeier and Maximilian Kiesner, and converted to a common format and to output tests for Julia by Oliver Heimlich.
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## Authors
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-[Luis Benet](http://www.cicc.unam.mx/~benet/), Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México (UNAM)
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-[David P. Sanders](http://sistemas.fciencias.unam.mx/~dsanders), Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)
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### Contributors
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- Oliver Heimlich
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- Nikolay Kryukov
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- John Verzani
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## Bibliography
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-*Validated Numerics: A Short Introduction to Rigorous Computations*, W. Tucker, Princeton University Press (2010)
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