Related papers: Mixed precision solvers with half-precision floati…
Some recent processors are not equipped with an integer division unit. Compilers then implement division by a call to a special function supplied by the processor designers, which implements division by a loop producing one bit of quotient…
A high fidelity flow simulation for complex geometries for high Reynolds number ($Re$) flow is still very challenging, which requires more powerful computational capability of HPC system. However, the development of HPC with traditional CPU…
We present a mixed-precision implementation of the high-order discontinuous Galerkin method with ADER time stepping (ADER-DG) for solving hyperbolic systems of partial differential equations (PDEs) in the hyperbolic PDE engine ExaHyPE. The…
By exploiting the modular RISC-V ISA this paper presents the customization of instruction set with posit\textsuperscript{\texttrademark} arithmetic instructions to provide improved numerical accuracy, well-defined behavior and increased…
The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…
Results of porting parts of the Lattice Quantum Chromodynamics code to modern FPGA devices are presented. A single-node, double precision implementation of the Conjugate Gradient algorithm is used to invert numerically the Dirac-Wilson…
This paper discusses a simple and effective method for the summation of long sequences of floating point numbers. The method comprises two phases: an accumulation phase where the mantissas of the floating point numbers are added to…
Enabling On-Device Learning (ODL) for Ultra-Low-Power Micro-Controller Units (MCUs) is a key step for post-deployment adaptation and fine-tuning of Deep Neural Network (DNN) models in future TinyML applications. This paper tackles this…
The Graphic Processing Unit (GPU) has evolved into a powerful and flexible processor. The latest graphic processors provide fully programmable vertex and pixel processing units that support vector operations up to single floating-point…
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…
Mixed precision training (MPT) is becoming a practical technique to improve the speed and energy efficiency of training deep neural networks by leveraging the fast hardware support for IEEE half-precision floating point that is available in…
Graphics Processing Units (GPUs) are having a transformational effect on numerical lattice quantum chromodynamics (LQCD) calculations of importance in nuclear and particle physics. The QUDA library provides a package of mixed precision…
The rapid updates in error-resilient applications along with their quest for high throughput have motivated designing fast approximate functional units for Field-Programmable Gate Arrays (FPGAs). Studies that proposed imprecise functional…
The state-of-the-art (SOTA) for mixed precision training is dominated by variants of low precision floating point operations, and in particular, FP16 accumulating into FP32 Micikevicius et al. (2017). On the other hand, while a lot of…
Since numbers in the computer are represented with a fixed number of bits, loss of accuracy during calculation is unavoidable. At high precision where more bits (e.g. 64) are allocated to each number, round-off errors are typically small.…
Modern graphics processing units (GPUs) provide impressive computing resources, which can be accessed conveniently through the CUDA programming interface. We describe how GPUs can be used to considerably speed up molecular dynamics (MD)…
Low-cost embedded processors such as the ESP32 (Xtensa LX6, 32-bit dual-core, 240 MHz) are increasingly used in edge computing applications that require real-time physical simulation, sensor fusion, and control systems. Although the ESP32…
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…
We present a non-iterative solver based on the Schur complement method for sparse linear systems of special form which appear in Quantum Monte-Carlo (QMC) simulations of strongly interacting fermions on the lattice. While the number of…
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution of least squares (LS) problems $\min_x\|b-Ax\|_2$, where $A…