Standard Article

Rounding Errors

  1. Jean-Marie Chesneaux,
  2. Stef Graillat,
  3. Fabienne Jézéquel

Published Online: 16 MAR 2009

DOI: 10.1002/9780470050118.ecse582

Wiley Encyclopedia of Computer Science and Engineering

Wiley Encyclopedia of Computer Science and Engineering

How to Cite

Chesneaux, J.-M., Graillat, S. and Jézéquel, F. 2009. Rounding Errors. Wiley Encyclopedia of Computer Science and Engineering. 2480–2494.

Author Information

  1. Laboratoire d'Informatique de Paris, France

Publication History

  1. Published Online: 16 MAR 2009

Abstract

Rounding errors present an inherent problem to all computer programs that involve floating-point numbers. They appear nearly in all elementary operations. By accumulation, these errors can affect the accuracy of a computed result possibly leading to some or total inaccuracy. First in this article, computer arithmetic that uses binary system and the IEEE standard for floating-point numbers is described together with some problems introduced by rounding errors. The effects of these rounding errors can be analyzed and studied by some methods like forward/backward analysis and interval or stochastic arithmetic. Finally, it is shown how the accuracy of the results can be improved by using compensated methods and multiprecision arithmetic.

Keywords:

  • rounding error;
  • floating-point arithmetic;
  • IEEE 754 standard;
  • accurate computation;
  • interval arithmetic;
  • stochastic arithmetic;
  • multiprecision