ValidatedNumerics.jl
is a suite of Julia packages for performing Validated Numerics in Julia, i.e. rigorous computations with finiteprecision floatingpoint 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.
The aims of the package are both correctness and good performance.
To install the package, from within Julia do
julia> Pkg.add("ValidatedNumerics")
Since version 0.9, ValidatedNumerics.jl
is a metapackage that automatically installs and reexports the following packages from the JuliaIntervals
GitHub organization:

IntervalArithmetic.jl
: arithmetic and elementary functions on intervals 
IntervalRootFinding.jl
: find roots of multidimensional functions in a guaranteed way 
IntervalOptimisation.jl
: guaranteed global optimisation of multidimensional functions 
IntervalConstraintProgramming.jl
: characterization of feasible sets of equations and inequalities via constraint propagation 
IntervalContractors.jl
: contractors and reverse (or inverse) functions 
TaylorModels.jl
: rigorous function approximation
The documentation for each of the above packages can be found here
The IEEE Std 17882015  IEEE Standard for Interval Arithmetic was published in June 2015. We are working towards having ValidatedNumerics
be conformant with this standard.
To do so, we have incorporated tests from the excellent ITF1788 test suite, originally written by Marco Nehmeier and Maximilian Kiesner, and converted to a common format and to output tests for Julia by Oliver Heimlich.
 Luis Benet, Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México (UNAM)
 David P. Sanders, Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)
 Validated Numerics: A Short Introduction to Rigorous Computations, W. Tucker, Princeton University Press (2010)
 Introduction to Interval Analysis, R.E. Moore, R.B. Kearfott & M.J. Cloud, SIAM (2009)
 MPFI.jl, a Julia wrapper around the MPFI C library, a multipleprecision interval arithmetic library based on MPFR
 Intervals.jl, an alternative implementation of basic interval functions.
This project was begun during a masters' course in the postgraduate programs in Physics and in Mathematics at UNAM during the second semester of 2013 (in Python  the ValidiPy
package), and was reinitiated  now in Julia  in the first semester of 2015. We thank the participants of the courses for putting up with the halfbaked material and contributing energy and ideas.
Financial support is acknowledged from DGAPAUNAM PAPIME grants PE105911 and PE107114, and DGAPAUNAM PAPIIT grants IN117214 and 117117. LB acknowledges support through a Cátedra Marcos Moshinsky (2013). DPS acknowledges a sabbatical fellowship from CONACYT and thanks Alan Edelman and the Julia group at MIT for hosting his sabbatical visit during 2016.