Next: Approaches to Exact Real Up: Approaches to Real Arithmetic Previous: Symbolic Approaches

## Exact Real Arithmetic

Exact real arithmetic is a numerical approach to real number computation based on potentially infinite data structures such as streams. Its main feature is that it solves the problems of inaccuracy and uncertainty in floating point and interval arithmetic, and is applicable in some cases in which a symbolic approach would not be appropriate.

Although exact real arithmetic can be used to calculate results which can be guaranteed to be completely accurate, it does so at the expense of the efficiency afforded by more conventional methods. One reason for this is that in practice, infinite data structures such as streams are inherently expensive to manage when compared with the type of fixed sized data structure used to represent floating point numbers. In addition, during exact computations it is often found that a small portion of the result of a computation may depend upon a large amount of the input. These inefficiencies assoociated with exact real arithmetic may be an acceptable trade-off against the benefits. For example which do not consider a sufficient number of digits to determine the correct result will be inherently inaccurate. These issues are discussed further in chapter 7.

Next: Approaches to Exact Real Up: Approaches to Real Arithmetic Previous: Symbolic Approaches
Martin Escardo
5/11/2000