MPFI.jl

MPFI.jl is a Julia wrapper for the MPFI (Multiple Precision Floating-Point Interval) C library, which provides interval arithmetic with arbitrary precision, based on MPFR. This package enables Julia users to perform high-precision interval computations seamlessly.

Features

• Arbitrary Precision: Perform interval arithmetic with precision limited only by available memory, thanks to MPFI’s reliance on MPFR.

• Compatibility: Ideal for users porting code from other languages that already use MPFI or MPFR.

• Validated Numerical Computations: Ensure reliable bounds for computations to maintain rigor in scientific and engineering applications.

• DynamicPolynomials Integration: You can use MPFI.jl in combination with the DynamicPolynomials package to create polynomials with interval coefficients, differentiate them, and evaluate them at other intervals.

Installation

To use the MPFI.jl package, install it using the repository's url:

julia> import Pkg; Pkg.add(url="https://gitlab.inria.fr/ckatsama/mpfi.jl.git");

julia> using MPFI

Quick Start

Here’s a simple example to get started with MPFI.jl:

julia> using MPFI

julia> a = BigInterval(1.0, 2.0)  
[1.0, 2.0]
julia> b = BigInterval(0.5, 1.5) 
[0.5, 1.5]

julia> sum = a + b  
[1.5, 3.5]
julia> product = a * b 
[0.5, 3.0]
julia> difference = a - b
[-0.5, 1.5]


julia> println("Lower bound of sum: ", left(sum))
Lower bound of sum: 1.5

julia> println("Upper bound of sum: ", right(sum))
Upper bound of sum: 3.5

julia> println("Intersection of intervals: ", MPFI.intersect(a, b))
Intersection of intervals: [1.0, 1.5]

julia> println("Union of intervals: ", MPFI.union(a, b))
Union of intervals: [0.5, 2.0]

julia> c = BigInterval(1//3;precision=14) # Define an interval by specifying its precision
[0.333312, 0.333344]
julia> precision(c)
14

julia> c = BigInterval(1//3) # Define an interval with the default precision of BigFloat
[0.3333333333333333333333333333333333333333333333333333333333333333333333333333304, 0.3333333333333333333333333333333333333333333333333333333333333333333333333333348]
julia> precision(c)
256

Documentation

The full documentation for the functions and usage of MPFI.jl can be found here.

License

MPFI.jl is licensed under the MIT License. See LICENSE for more details.

References

• MPFI C library documentation