Does the computer really calculate accurately?

Written by Sethy Montan, on 06 February 2018

This article introduces the issue of the numerical quality of computer calculations. We are particularly interested in the concept of rounding errors in calculations and the potential consequences they can entail.

Raising Awareness of Numerical Precision Issues

The computer has become an indispensable and essential element of our daily lives. For instance, the weather forecasts presented by Evelyne Dheliat are based on estimations made by software. Using a multitude of data, this type of software (known as numerical simulation software) performs calculations to predict tomorrow's temperature, model the optimal shape of an airplane, estimate the duration of our journey to the airport, or the trajectory of a rocket... In essence, our daily lives depend on numerical simulations made through computer calculations. Therefore, it is important to ensure the quality and reliability of these calculations. Note that several types of errors can influence the reliability of calculations: machine malfunctions especially in difficult conditions (nuclear radiation...), and errors by developers, meaning discrepancies between the expected behavior and the actual behavior of the software. These discrepancies are generally due to illegal operations (bad memory access, division by 0, access to non-existent data...), logic problems (forgetting/bad handling of a situation...), and the numerical precision of calculations. In this article, we introduce the concept of numerical quality of computer calculations. We show that in some cases (or generally), it is not always satisfactory.

A Matter of Tenths of a Second...

Our objective here is to raise awareness about the issues regarding the quality of results of calculations performed by a computer, and especially their consequences. Indeed, history has already shown us that these types of problems, although often neglected, can generate enormous consequences (Douglas, 1998). For example, let's mention the failure of the Patriot anti-missile system during the first Gulf War, which resulted in the death of about twenty people.