Related papers: Fast Floating-Point Filters for Robust Predicates
Deductive verification has been successful in verifying interesting properties of real-world programs. One notable gap is the limited support for floating-point reasoning. This is unfortunate, as floating-point arithmetic is particularly…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
Robust parameter estimation is a crucial task in several 3D computer vision pipelines such as Structure from Motion (SfM). State-of-the-art algorithms for robust estimation, however, still suffer from difficulties in converging to…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
Current critical systems commonly use a lot of floating-point computations, and thus the testing or static analysis of programs containing floating-point operators has become a priority. However, correctly defining the semantics of common…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
Pipelined algorithms implemented in field programmable gate arrays are being extensively used for hardware triggers in the modern experimental high energy physics field and the complexity of such algorithms are increases rapidly. For…
We introduce data structures and algorithms to count numerical inaccuracies arising from usage of floating numbers described in IEEE 754. Here we describe how to estimate precision for some collection of functions most commonly used for…
Noisy, partially overlapping data and the need for real-time processing pose major challenges for rigid registration. Considering that feature-based matching can handle large transformation differences but suffers from limited accuracy,…
Many algorithms used are based on geometrical computation. There are several criteria in selecting appropriate algorithm from already known. Recently, the fastest algorithms have been preferred. Nowadays, algorithms with a high stability…
Reliable numerical computations are central to scientific computing, but the floating-point arithmetic that enables large-scale models is error-prone. Numeric exceptions are a common occurrence and can propagate through code, leading to…
Block Floating Point (BFP) arithmetic is currently seeing a resurgence in interest because it requires less power, less chip area, and is less complicated to implement in hardware than standard floating point arithmetic. This paper explores…
Researchers have developed neural network verification algorithms motivated by the need to characterize the robustness of deep neural networks. The verifiers aspire to answer whether a neural network guarantees certain properties with…
Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of…
Two-dimensional Delaunay triangulation is a fundamental aspect of computational geometry. This paper presents a novel algorithm that is specifically designed to ensure the correctness of 2D Delaunay triangulation, namely the Polygonal…
Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…
Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction, that is, we present examples in which…
We analyse the complexity of computing class polynomials, that are an important ingredient for CM constructions of elliptic curves, via complex floating point approximations of their roots. The heart of the algorithm is the evaluation of…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
Quantum algorithms to solve practical problems in quantum chemistry, materials science, and matrix inversion often involve a significant amount of arithmetic operations which act on a superposition of inputs. These have to be compiled to a…