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Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has…

Mathematical Software · Computer Science 2017-10-06 Tomonori Kouya

Deep learning has become a useful data analysis method, however mainstream adaption in distributed computer software and embedded devices has been low so far. Often, adding deep learning inference in mainstream applications and devices…

Machine Learning · Computer Science 2022-10-03 Fabian Tschopp

The growing availability and usage of low precision foating point formats has attracts many interests of developing lower or mixed precision algorithms for scientific computing problems. In this paper we investigate the possibility of…

Numerical Analysis · Mathematics 2024-02-14 Haibo Li

Current Python programming environment does not have any reliable and efficient multiple precision floating-point (MPF) arithmetic except ``mpmath" and ``gmpy2" packages based on GNU MP(GMP) and MPFR libraries. Although it is well known…

Mathematical Software · Computer Science 2021-07-28 Tomonori Kouya

Modern computer architectures support low-precision arithmetic, which present opportunities for the adoption of mixed-precision algorithms to achieve high computational throughput and reduce energy consumption. As a growing number of…

Computation · Statistics 2024-12-02 Sahil Bhola , Karthik Duraisamy

In todays world, high-power computing applications such as image processing, digital signal processing, graphics, and robotics require enormous computing power. These applications use matrix operations, especially matrix multiplication.…

Hardware Architecture · Computer Science 2019-10-29 Arish S , R. K. Sharma

The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…

Numerical Analysis · Mathematics 2024-03-19 Cody J. Balos , Steven Roberts , David J. Gardner

Recent advances in deep learning (DL) have led to a shift from traditional 64-bit floating point (FP64) computations toward reduced-precision formats, such as FP16, BF16, and 8- or 16-bit integers, combined with mixed-precision arithmetic.…

Computation and Language · Computer Science 2025-06-16 Héctor Martínez , Adrián Castelló , Francisco D. Igual , Enrique S. Quintana-Ortí

In recent years the computational capacity of single Field Programmable Gate Arrays (FPGA) devices as well as their versatility has increased significantly. Adding to that the High Level Synthesis frameworks allowing to program such…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-07-22 G. Korcyl , P. Korcyl

Lattice spin models are useful for studying critical phenomena and allow the extraction of equilibrium and dynamical properties. Simulations of such systems are usually based on Monte Carlo (MC) techniques, and the main difficulty is often…

Computational Physics · Physics 2012-09-13 Tal Levy , Guy Cohen , Eran Rabani

Graphics Processing Units (GPUs) are being used in many areas of physics, since the performance versus cost is very attractive. The GPUs can be addressed by CUDA which is a NVIDIA's parallel computing architecture. It enables dramatic…

High Energy Physics - Lattice · Physics 2012-10-12 Nuno Cardoso , Marco Cardoso , Pedro Bicudo

We study the implementation of the even-odd Wilson fermion matrix for lattice QCD simulations on the A64FX architecture. Efficient coding of the stencil operation is investigated for two-dimensional packing to SIMD vectors. We measure the…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-03-16 Issaku Kanamori , Keigo Nitadori , Hideo Matsufuru

Convolutional Neural Networks (CNNs) have been utilised in many image and video processing applications. The convolution operator, also known as a spatial filter, is usually a linear operation, but this linearity compromises essential…

Hardware Architecture · Computer Science 2024-09-10 Nelson Campos , Eran Edirisinghe , Salva Chesnokov , Daniel Larkin

Multigrid methods are popular iterative methods for solving large-scale sparse systems of linear equations. We present a mixed precision formulation of the multigrid V-cycle with general assumptions on the finite precision errors coming…

Numerical Analysis · Mathematics 2025-11-07 Petr Vacek , Hartwig Anzt , Erin Carson , Nils Kohl , Ulrich Rüde , Yu-Hsiang Tsai

We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…

Numerical Analysis · Mathematics 2024-05-07 Jean-Michel Muller , Bruno Salvy

We present the algorithms for three popular methods: F-expansion, modified F-expansion, and first integral methods to automatically get closed-form traveling-wave solutions of nonlinear partial differential equations (NLPDEs). We generalize…

Computational Physics · Physics 2023-04-18 Mithun Bairagi

This article presents a pioneering approach to real-time spacecraft pose estimation, utilizing a mixed-precision quantized neural network implemented on the FPGA components of a commercially available Xilinx MPSoC, renowned for its…

Computer Vision and Pattern Recognition · Computer Science 2024-07-09 Julien Posso , Guy Bois , Yvon Savaria

The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-05-18 Roman Iakymchuk , Maria Barreda , Stef Graillat , Jose I. Aliaga , Enrique S. Quintana-Orti

The hardware diversity in leadership-class computing facilities, alongside the immense performance boosts from today's GPUs when computing in lower precision, incentivizes scientific HPC workflows to adopt mixed-precision algorithms and…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-10-06 Sreeram Venkat , Kasia Swirydowicz , Noah Wolfe , Omar Ghattas

Scientific machine learning (SciML) has emerged as a versatile approach to address complex computational science and engineering problems. Within this field, physics-informed neural networks (PINNs) and deep operator networks (DeepONets)…

Machine Learning · Computer Science 2024-01-31 Joel Hayford , Jacob Goldman-Wetzler , Eric Wang , Lu Lu