Related papers: Multigrid Methods using Block Floating Point Arith…

Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…

In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…

Recent research has shown that large language models (LLMs) can utilize low-precision floating point (FP) quantization to deliver high efficiency while maintaining original model accuracy. In particular, recent works have shown the…

We investigate the use of half-precision floating-point numbers (FP16) in mixed-precision linear solvers for lattice QCD simulations. Since the emergence of GPUs for general-purpose, mixed-precision algorithms that combine single-precision…

Compression of floating-point data will play an important role in high-performance computing as data bandwidth and storage become dominant costs. Lossy compression of floating-point data is powerful, but theoretical results are needed to…

Mixed-precision quantization is a popular approach for compressing deep neural networks (DNNs). However, it is challenging to scale the performance efficiently with mixed-precision DNNs given the current FPGA architecture and conventional…

Floating point arithmetic remains expensive on FPGA platforms due to wide datapaths and normalization logic, motivating alternative representations that preserve dynamic range at lower cost. This work introduces the Hybrid Residue Floating…

In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric second-order linear elliptic diffusion problems. We show that…

For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the…

Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs is due to the peculiarities of floating-point arithmetic: rounding errors, infinities,…

Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…

For successful deployment of deep neural networks on highly--resource-constrained devices (hearing aids, earbuds, wearables), we must simplify the types of operations and the memory/power resources used during inference. Completely avoiding…

In the current work, a number of algorithms are developed and compared for the numerical solution of periodic (quasi-static) linear elastic mechanical boundary-value problems (BVPs) based on two different discretizations of Fourier series.…

This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…

The acceleration of deep-learning kernels in hardware relies on matrix multiplications that are executed efficiently on Systolic Arrays (SA). To effectively trade off deep-learning training/inference quality with hardware cost, SA…

Reduced precision computation for deep neural networks is one of the key areas addressing the widening compute gap driven by an exponential growth in model size. In recent years, deep learning training has largely migrated to 16-bit…

This paper presents a novel algorithm for the modulus operation for FPGA implementation. The proposed algorithm use only addition, subtraction, logical, and bit shift operations, avoiding the complexities and hardware costs associated with…

The logarithmic number system (LNS) is arguably not broadly used due to exponential circuit overheads for summation tables relative to arithmetic precision. Methods to reduce this overhead have been proposed, yet still yield designs with…

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…

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…