Supercomputers are now so fast that they sacrifice accuracy for speed, and the resulting rounding errors differ between machines—meaning the same calculation can give different answers on different devices. This matters because modern high-performance computers, like the Met Office’s machine that processes 215 billion weather observations daily, are used for critical public simulations. But hardware designers take undocumented shortcuts—varying how many digits they use or how they round numbers—so results are not reproducible across devices. Current methods to detect these hidden numerical features require manual, highly specialised mathematical work, and must be rewritten for each new processor. This project aims to automate that detection, remove the need for expert knowledge, and build a publicly accessible library of known hardware behaviours. If successful, it will let engineers and scientists predict how a new chip will behave before running their code. The tools could also serve as a compliance test as the industry moves toward standardising mathematical hardware over the next decade. The work is fundamental—it does not directly improve a weather forecast tomorrow—but without it, the growing gap between hardware speed and reliability will undermine trust in any simulation that depends on reproducible arithmetic.
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High performance computing (HPC) is an essential tool for science and society. From weather forecasting to large-scale data analysis, HPC enables efficient simulations and predictions. At the fundamental level high-performance computers are good at performing many basic operations, such as addition and multiplication, upon which more complicated operations and applications are built. As an example, the fastest supercomputer in the TOP500 list, Frontier, has almost 9 million processors and has been observed to perform ~1.1 * 10^18 operations per second. In the push for performance, high-performance computing often trades off accuracy for speed, by simplifying basic building blocks in the hardware and increasing the rounding errors induced in the basic operations. The shortcuts taken by the hardware designers can make devices diverge from the standard well-known behaviour, and often the differences are not documented. Two pieces of hardware from different manufacturers may perform operations at different speeds and give different results, because designers implement features such as rounding differently or use a different number of digits in adding and multiplying. Due to this, applications are not reproducible and we cannot predict in advance what will happen on a new device. We now understand well that the hardware from 2016 onwards started along this path. As we are running various computations directly relevant to the public on these computers, such as climate and weather simulations, the discrepancy between devices requires investigation through a systematic study. For example, Met Office in Exeter have a high-performance computer that allows them to make 215 billion weather observations from all over the world every day. Computer Scientists and Mathematicians have come up with ways to run carefully designed programs that inform us about the underlying numerical features of the devices, such as rounding or precision of calculations. However, the state-of-the-art approach involves a lot of manual work based on very specialized mathematical knowledge. It is prone to human errors—when new devices appear, engineers have to change the software to determine what differences they have compared with the previous devices. This project is about improving the existent methods, by focusing on three core aspects: automating, removing the need for specialized knowledge, and informing the public about the features of the current hardware. In more detail, the project has three main outcomes: theoretical methods to search for undocumented hardware’s mathematical features automatically; a library of known behaviours of hardware, which will be publicly available and continuously updated by us and the community that we will develop, as the hardware is converging to standardisation over the next decade; and software that can report numerical features to users, which will not require highly specialised knowledge. These outcomes will impact the industry that is creating mathematical hardware, the users that depend on the accuracy and consistency of it and are not always getting that due to the shift in how the hardware is designed, and ultimately the standardisation of mathematical hardware. As hardware converges to standardisation in the next decade, the tools developed in this project will become a test for compliance.
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