48 citations · 48 across the 13 of their papers we have counts for
17 papers
Analysis and Detection of Stagnation in Floating-Point Summation
Mantas Mikaitis, William Woolfenden
Stagnation in the summation of floating-point numbers occurs when the running sum, or the accumulator, does not change its value despite addends being greater than zero. Here we de…
Mixed-Precision Computing for Scientific Discovery: Formats, Co-Design, and Responsible Approximation
Emmanuel Agullo, Hartwig Anzt, Daniel Bauer +37
Reduced and mixed precision have moved from a niche optimization to a central design axis in scientific computing and engineering, driven by energy constraints, heterogeneous accel…
Accurate Models of AMD Matrix Cores
Faizan A Khattak, Mantas Mikaitis, Carlo J. Graziani
Matrix multipliers available on recent GPUs do not conform with the IEEE 754 floating point standard. Features of matrix multipliers differ across vendors and architectures of the…
The SpiNNaker2 chip: a many-core platform for flexible and scalable brain-inspired computing
Stefan Scholze, Johannes Partzsch, Sebastian Höppner +27
In deep learning, efficiency gets more and more important to compensate for the ongoing growth in model sizes and applications. Neuromorphic hardware has long been advocated as an…
Simulation of Custom-Precision OCP MX Block Floating-Point Formats and Arithmetic
Maliha Islam, Mantas Mikaitis
We present MXsim v0.1: a MATLAB library for simulating the OCP MX block floating-point arithmetic and formats. The library is built on top of a custom-precision floating-point simu…
Probabilistic Error Analysis of Limited-Precision Stochastic Rounding: Horner's Algorithm and Pairwise Summation
El-Mehdi El Arar, Massimiliano Fasi, Silviu-Ioan Filip +1
Stochastic rounding (SR) is a probabilistic rounding mode that mitigates errors in large-scale numerical computations, especially when prone to stagnation effects. Beyond numerical…
What is New in Stochastic Rounding: a Survey on Theory, Hardware, and Applications
El-Mehdi El Arar, Massimiliano Fasi, Silviu-Ioan Filip +1
Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length summation, the worst-case error of SR grow…
Accurate Models of NVIDIA Tensor Cores
Faizan A. Khattak, Mantas Mikaitis
Matrix multiplication is a fundamental operation in both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide i…
Generalized Methodology for Determining Numerical Features of Hardware Floating-Point Matrix Multipliers: Part I
Faizan A Khattak, Mantas Mikaitis
Numerical features of matrix multiplier hardware units in NVIDIA and AMD data centre GPUs have recently been studied. Features such as rounding, normalisation, and internal precisi…
Accuracy of Mathematical Functions in Julia
Mantas Mikaitis, Mosè Giordano, Tejaswa Rizyal
Basic computer arithmetic operations, such as , , or are correctly rounded, whilst mathematical functions such as , , or in general are not, m…
Analysis of Floating-Point Matrix Multiplication Computed via Integer Arithmetic
Ahmad Abdelfattah, Jack Dongarra, Massimiliano Fasi +2
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer…
Probabilistic error analysis of limited-precision stochastic rounding
El-Mehdi El Arar, Massimiliano Fasi, Silviu-Ioan Filip +1
Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms th…
MATLAB Simulator of Level-Index Arithmetic
Mantas Mikaitis
Level-index arithmetic appeared in the 1980s. One of its principal purposes is to abolish the issues caused by underflows and overflows in floating point. However, level-index arit…
Monotonicity of Multi-Term Floating-Point Adders
Mantas Mikaitis
In the literature on algorithms for performing the multi-term addition using floating-point arithmetic it is often shown that a hardware unit that has single…
Stochastic Rounding: Algorithms and Hardware Accelerator
Mantas Mikaitis
Algorithms and a hardware accelerator for performing stochastic rounding (SR) are presented. The main goal is to augment the ARM M4F based multi-core processor SpiNNaker2 with a mo…
Issues with rounding in the GCC implementation of the ISO 18037:2008 standard fixed-point arithmetic
Mantas Mikaitis
We describe various issues caused by the lack of round-to-nearest mode in the \textit{gcc} compiler implementation of the fixed-point arithmetic data types and operations. We demon…
Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations
Michael Hopkins, Mantas Mikaitis, Dave R. Lester +1
Although double-precision floating-point arithmetic currently dominates high-performance computing, there is increasing interest in smaller and simpler arithmetic types. The main r…