Compromise between precision and performance in high performance computing.

Floating-point numbers represent only a subset of real numbers. As such, floating-point arithmetic introduces approximations that can compound and have a significant impact on numerical simulations. We introduce a new way to estimate and localize the sources of numerical error in an application and provide a reference implementation, the Shaman library. Our method uses a dedicated arithmetic over a type that encapsulates both the result the user would have had with the original computation and an approximation of its numerical error. We thus can measure the number of significant digits of any result or intermediate result in a simulation. We show that this approach, while simple, gives results competitive with state-of-the-art methods. It has a smaller overhead and is compatible with parallelism which makes it suitable for the study of large scale applications.