Moore: Interval Arithmetic in C++20

Mascarenhas, Walter F.

doi:10.1007/978-3-319-95312-0_45

Cited by 6 publications

(7 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our slight improvement comes in the way we compute the intersections in Equations (13). These intersections are 1 := − / and 2 := − / , and, as usual in the Moore Library [8], we propose that 1 and 2 be computed with the rounding mode upwards, using the following expressions:…”

Section: The Interval Version Of Newton's Stepmentioning

confidence: 99%

See 1 more Smart Citation

Root Finding With Interval Arithmetic

Mascarenhas

2021

Preprint

View full text Add to dashboard Cite

We consider the solution of nonlinear equations in one real variable, the problem usually called by root finding. Although this is an old problem, we believe that some aspects of its solution using interval arithmetic are not well understood, and we present our views on this subject. We argue that problems with just one variable are much simpler than problems with more variables, and we should use specific methods for them. We provide an implementation of our ideas in C++, and make this code available under the Mozilla Public License 2.0.

show abstract

Section: The Interval Version Of Newton's Stepmentioning

confidence: 99%

“…We implemented the algorithm outlined above in C++, using our Moore interval arithmetic library [8]. This code is available with the arxiv version of this article.…”

mentioning

confidence: 99%

Root Finding With Interval Arithmetic

Mascarenhas

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Algorithm 1 summarizes the interval branch-and-bound method. We implement the algorithm in C++ using two interval arithmetic libraries, the Filib [14] and the Moore [17]. The user can choose any of these implementations in the verification of the proof.…”

Section: The Algorithmmentioning

confidence: 99%

Rigorous packing of unit squares into a circle

et al. 2018

View full text Add to dashboard Cite

This paper considers the task of finding the smallest circle into which one can pack a fixed number of non-overlapping unit squares that are free to rotate. Due to the rotation angles, the packing of unit squares into a container is considerably harder to solve than their circle packing counterparts. Therefore, optimal arrangements were so far proved to be optimal only for one or two unit squares. By a computer-assisted method based on interval arithmetic techniques, we solve the case of three squares and find rigorous enclosures for every optimal arrangement of this problem. We model the relation between the squares and the circle as a constraint satisfaction problem (CSP) and found every box that may contain a solution inside a given upper bound of the radius. Due to symmetries in the search domain, general purpose interval methods are far too slow to solve the CSP directly. To overcome this difficulty, we split the problem into a set of subproblems by systematically adding constraints to the center of each square. Our proof requires the solution of 6, 43 and 12 subproblems with 1, 2 and 3 unit squares respectively. In principle, the method proposed in this paper generalizes to any number of squares. Electronic supplementary material The online version of this article (10.1007/s10898-018-0711-5) contains supplementary material, which is available to authorized users.

show abstract

“…This problem has applications in economics and computational geometry [2], but we developed the data structure and algorithm presented here for finding rigorous bounds on the solutions of two dimensional nonlinear programming problems using interval arithmetic [4]. For instance, when using Newton's method to solve a nonlinear system of equations ( ) = 0 for : R 2 → R 2 with branch and bound, in each branch we have a candidate set of solutions S described by a family of inequalities as in Equation (1).…”

Section: Introductionmentioning

confidence: 99%

Solving systems of inequalities in two variables with floating point arithmetic

Mascarenhas

2021

Preprint

View full text Add to dashboard Cite

From a theoretical point of view, finding the solution set of a system of inequalities in only two variables is easy. However, if we want to get rigorous bounds on this set with floating point arithmetic, in all possible cases, then things are not so simple due to rounding errors. In this article we describe in detail an efficient data structure to represent this solution set and an efficient and robust algorithm to build it using floating point arithmetic. The data structure and the algorithm were developed as a building block for the rigorous solution of relevant practical problems. They were implemented in C++ and the code was carefully tested. This code is available as supplementary material to the arxiv version of this article, and it is distributed under the Mozilla Public License 2.0.

show abstract

Moore: Interval Arithmetic in C++20

Abstract: This article presents the Moore library for interval arithmetic in C++20. It gives examples of how the library can be used, and explains the basic principles underlying its design.

Cited by 6 publications

References 11 publications

Root Finding With Interval Arithmetic

Root Finding With Interval Arithmetic

Rigorous packing of unit squares into a circle

Solving systems of inequalities in two variables with floating point arithmetic

Contact Info

Product

Resources

About