Related papers: Fast Floating-Point Filters for Robust Predicates

Delaunay Triangulation(DT) is one of the important geometric problems that is used in various branches of knowledge such as computer vision, terrain modeling, spatial clustering and networking. Kinetic data structures have become very…

Programs with floating-point computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floating-point numbers may differ from the…

We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our…

Floating-point arithmetic performance determines the overall performance of important applications, from graphics to AI. Meeting the IEEE-754 specification for floating-point requires that final results of addition, subtraction,…

We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…

Over the last few years, neural networks have started penetrating safety critical systems to take decisions in robots, rockets, autonomous driving car, etc. A problem is that these critical systems often have limited computing resources.…

We present a generic C++ design to perform efficient and exact geometric computations using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also critical for most…

Floating-point programs form the foundation of modern science and engineering, providing the essential computational framework for a wide range of applications, such as safety-critical systems, aerospace engineering, and financial analysis.…

This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLibm approach that frames the problem of generating correctly rounded libraries as a linear programming…

An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…

The computation of determinants or their signs is the core procedure in many important geometric algorithms, such as convex hull, volume and point location. As the dimension of the computation space grows, a higher percentage of the total…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…

Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…

Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…

Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…

This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…

Program verification techniques typically focus on finding counter-examples that violate properties of a program. Constraint programming offers a convenient way to verify programs by modeling their state transformations and specifying…

In this work, we provide energy-efficient architectural support for floating point accuracy. Our goal is to provide accuracy that is far greater than that provided by the processor's hardware floating point unit (FPU). Specifically, for…

Reasoning about floating-point arithmetic is notoriously hard. While static and dynamic analysis techniques or program repair have made significant progress, more work is still needed to make them relevant to real-world code. On the…