Algorithms in scientific computing often use real numbers. However, it is not possible for computing units to work directly with real numbers, whose representation may show an infinite number of digits. This is why floating-point arithmetic has emerged as the best compromise between the performance of the computing units and the approximation of the calculated results.

Nevertheless, floating-point arithmetic can only work with finite precision and therefore behaves significantly differently from real arithmetic. The aim of this course is to familiarise the trainees with topics related to the use of floating-point arithmetic in scientific computing codes. First, we will familiarise ourselves with floating-point arithmetic in order to understand the origin of the problems it can cause. We will then see what techniques and tools are available to diagnose, quantify and debug the errors and losses of reproducibility induced by floating-point arithmetic. Finally, we will discuss techniques for correcting the problems discovered, with minimal impact on the performance of the computational tools.