From climate to medical imaging: why is the reliability of numerical calculations crucial?

Numerical calculations sometimes limited

Apart from whole numbers, computers use floating point numbers, with rounding. These are therefore approximations of real numbers.

Since 1985, the international standard IEEE 754 has governed these operations. It defines how to represent floating point numbers and how to round the results. For basic operations (addition, subtraction, multiplication, division and square root), the standard imposes the principle of correct rounding. Once the rounding mode has been chosen, a given calculation produces a single possible result, identical on all machines.

This mechanism is essential because it guarantees the reproducibility of calculations, a pillar of any scientific approach.

However, the IEEE 754 standard has one significant limitation: it does not set any correct rounding rules for more complex mathematical functions (such as exponential, logarithmic, sine or power functions).

In practice, this means that the same calculation can produce different results depending on the mathematical library used, or even depending on the version of that library. Even when the user explicitly requests a rounding mode, the result obtained may not be correct.

These seemingly minor discrepancies have real consequences. Research has shown that in neuroimaging, for example, the choice of mathematical library can lead to significantly different images.

In meteorology or climatology, where calculations are lengthy and crucial, slight rounding errors can propagate and alter the final results.

CORE-MATH: making calculations reliable and reproducible

The CORE-MATH project was launched in 2022 with the aim of providing open source reference implementations that guarantee correct rounding for common mathematical functions, in accordance with the spirit of the IEEE 754 standard.

This means that users can choose a rounding mode and obtain the mathematically correct result, regardless of their software or hardware environment. Calculations then become strictly reproducible.

This project follows on from the work of Jean-Michel Muller, an Inria researcher and winner of the 2024 Inria Grand Prix for his major contributions to floating-point arithmetic.

While his research laid the theoretical foundations for correct rounding, CORE-MATH provides a concrete demonstration of this: it shows that it is possible to calculate correctly without sacrificing performance, a decisive factor for industrial and scientific adoption.

An open source project for European digital sovereignty

CORE-MATH does not aim to create a new library, but rather to provide reference implementations intended for integration into existing libraries. Entirely open source under the MIT licence, the project promotes widespread distribution, transparent calculations and increased confidence in digital tools.

By providing open and verifiable mathematical foundations, CORE-MATH also contributes to European digital sovereignty in areas where calculation reliability is strategic: health, climate, energy and scientific research.

First concrete results

The progress made is already tangible. Around thirty single-precision functions from CORE-MATH have been integrated into the GNU standard library. Seven double-precision functions were published in January 2026. Other libraries, particularly industrial ones, are also beginning to adopt this work.

The main challenge remains efficiency: to be widely used, these implementations must be as fast as existing solutions. This is a key issue for the future of the project.