Related papers: Custom-Precision Mathematical Library Explorations…
A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…
Sparse linear algebra is central to many scientific programs, yet compilers fail to optimize it well. High-performance libraries are available, but adoption costs are significant. Moreover, libraries tie programs into vendor-specific…
We describe lrsarith which is a small fixed precision and hybrid arithmetic C library for integers and rationals that we developed for use in the lrslib library for polyhedral computation. Using a generic set of operations, a program can be…
Single-precision floating point (FP32) data format, defined by the IEEE 754 standard, is widely employed in scientific computing, signal processing, and deep learning training, where precision is critical. However, FP32 multiplication is…
Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause…
In the software development required a fidelity and accuracy in determining the size or value of the software to fit the operation is executed. Various methods of calculation has been widely applied to estimate the size, and one of them is…
Interval computation is widely used to certify computations that use floating point operations to avoid pitfalls related to rounding error introduced by inaccurate operations. Despite its popularity and practical benefits, support for…
Deploying neural networks on edge devices entails a careful balance between the energy required for inference and the accuracy of the resulting classification. One technique for navigating this tradeoff is approximate computing: the process…
In this paper, we propose an architecture/methodology for making FPGAs suitable for integer as well as variable precision floating point multiplication. The proposed work will of great importance in applications which requires variable…
Reliable parameter extraction from experimental data is central to quantitative analysis in spectroscopy, diffraction, photoluminescence, chromatography, microscopy, and time-resolved measurements. We present FitED, a Python-based desktop…
The computation of exact barycenters for a set of discrete measures is of interest in applications where sparse solutions are desired, and to assess the quality of solutions returned by approximate algorithms and heuristics. The task is…
We introduce cilantro, an open-source C++ library for geometric and general-purpose point cloud data processing. The library provides functionality that covers low-level point cloud operations, spatial reasoning, various methods for point…
Finite-precision arithmetic computations face an inherent tradeoff between accuracy and efficiency. The points in this tradeoff space are determined, among other factors, by different data types but also evaluation orders. To put it simply,…
This report provides an introduction to the ensmallen numerical optimization library, as well as a deep dive into the technical details of how it works. The library provides a fast and flexible C++ framework for mathematical optimization of…
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 study the multiple-precision addition of two positive floating-point numbers in base 2, with exact rounding, as specified in the MPFR library, i.e. where each number has its own precision. We show how the best possible complexity (up to…
Post-training quantization (PTQ) is a powerful technique for model compression, reducing the numerical precision in neural networks without additional training overhead. Recent works have investigated adopting 8-bit floating-point…
Scientific software is often driven by multiple parameters that affect both accuracy and performance. Since finding the optimal configuration of these parameters is a highly complex task, it extremely common that the software is used…
Fine-grained memory protection for C and C++ programs must track individual objects (or pointers), and store bounds information per object (pointer). Its cost is dominated by metadata updates and lookups, making efficient metadata…
We show that the effects of finite-precision arithmetic in forming and solving the linear system that arises at each iteration of primal-dual interior-point algorithms for nonlinear programming are benign, provided that the iterates satisfy…