Related papers: New Developments in Interval Arithmetic and Their …
An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically…
Gappa uses interval arithmetic to certify bounds on mathematical expressions that involve rounded as well as exact operators. Gappa generates a theorem with its proof for each bound treated. The proof can be checked with a higher order…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
The problem of exactly generating a general random process (target process) by using another general random process (coin process) is studied. The performance of the interval algorithm, introduced by Han and Hoshi, is analyzed from the…
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…
Some recent processors are not equipped with an integer division unit. Compilers then implement division by a call to a special function supplied by the processor designers, which implements division by a loop producing one bit of quotient…
Our goal is to find accurate and efficient algorithms, when they exist, for evaluating rational expressions containing floating point numbers, and for computing matrix factorizations (like LU and the SVD) of matrices with rational…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
Multiplication of n-digit integers by long multiplication requires O(n^2) operations and can be time-consuming. In 1970 A. Schoenhage and V. Strassen published an algorithm capable of performing the task with only O(n log(n)) arithmetic…
The Smatch metric is a popular method for evaluating graph distances, as is necessary, for instance, to assess the performance of semantic graph parsing systems. However, we observe some issues in the metric that jeopardize meaningful…
In this thesis, work is undertaken towards the design in hardware description languages and implementation in FPGA of an out-of-order execution engine of floating-point arithmetic operations for the Lagarto II core. A first proposal covers…
Geometric predicates are a basic ingredient to implement a vast range of algorithms in computational geometry. Modern implementations employ floating point filtering techniques to combine efficiency and robustness, and state-of-the-art…
Floating-point accumulation networks (FPANs) are key building blocks used in many floating-point algorithms, including compensated summation and double-double arithmetic. FPANs are notoriously difficult to analyze, and algorithms using…
We describe various issues caused by the lack of round-to-nearest mode in the \textit{gcc} compiler implementation of the fixed-point arithmetic data types and operations. We demonstrate that round-to-nearest is not performed in the…
To obtain accurate results in numerical computation, high-precision arithmetic is a straightforward approach. However, most processors lack hardware support for floating-point formats beyond double precision (FP64). Double-word arithmetic…
Floating point division, even though being an infrequent operation in the traditional sense, is indis- pensable when it comes to a range of non-traditional applications such as K-Means Clustering and QR Decomposition just to name a few. In…
Inspired by computer assisted proofs in analysis, we present an interval approach to real-number computations.
Numerous purportedly improved metaheuristics claim superior performance based on equivalent function evaluations (FEs), yet often conceal additional computational burdens in more intensive iterations, preprocessing stages, or hyperparameter…
In recent years, half precision floating-point arithmetic has gained wide support in hardware and software stack thanks to the advance of artificial intelligence and machine learning applications. Operating at half precision can…
In recent work, Lemire (2021) presented a fast algorithm to convert number strings into binary floating-point numbers. The algorithm has been adopted by several important systems: e.g., it is part of the runtime libraries of GCC 12, Rust…