Exploration of Low Precision Numerical Hardware and Stochastic Rounding

   Faculty of Engineering and Physical Sciences

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  Dr Mantas Mikaitis  No more applications being accepted  Funded PhD Project (UK Students Only)

About the Project

Project Start Date: No later than 1 July 2024

In 1985 a floating-point standard has been introduced, which, among multiple things, defined a set of required and recommended arithmetic operations and mathematical functions. It is arguably the most important standard in the history of computing. Most computer processors and mathematical libraries adopted the standard, which in turn improved reproducibility between different versions of hardware or even between hardware from different vendors. Two subsequent revisions of the standard have been released, in 2008 and in 2019.

For decades the behaviour of 64-bit (double precision) and 32-bit (single precision) arithmetic has been relatively stable and predictable, with software developers being confident in achieving bit reproducibility in most cases. The latest TOP500 supercomputer list contains 158 machines with NVIDIA or AMD vector and matrix arithmetic operations, which diverge from the IEEE 754. Furthermore, rounding methods that are not standard, such as stochastic rounding, are being included in hardware: Graphcore IPU, Amazon Trainium, and Tesla Dojo chips. Most of the low precision arithmetic, despite being introduced for machine learning, are used in scientific computing in general for mixed precision algorithms.

This sudden change in numerical hardware (at the time of writing still ongoing), a fundamental feature of computers, presents new challenges. We need to develop methods to understand or test the numerical behaviour in order to be able to document it for each new device. It is important to understand the behaviour of software when creating new devices as well as when simulating the current ones. We also need to consider how to adapt our software to effectively use the low precision hardware, minimizing the effects of non-standard numerical operations. Finally, we should study how to combine these results to drive the standardization of low precision hardware in order to obtain consistent behaviour in the future.

Specific topics/projects within this general area will be tailored to individual interests and skills. Individual projects can be focused on software, hardware, or mathematical study, with possibilities for overlap. Please feel free to contact the main supervisor informally with your CV and a short list of interests for a discussion.

Computer Science (8) Mathematics (25)

Funding Notes

A highly competitive School of Computing Studentship consisting of the award of fees at the UK fee rate with a maintenance grant (currently £18,622 for session 2023/24) for 3.5 years. This opportunity is open to UK applicants only. All candidates will be placed into the School of Computing Studentship Competition and selection is based on academic merit.

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