Floating Point/Rounding

From Wikibooks, open books for an open world
< Floating Point
Jump to: navigation, search

Rounding[edit]

IEEE 754 specified four distinct rounding modes. We will talk about those modes, and their effects in this chapter. Also, rounding can play an important role in the accuracy of a floating-point computation, so we will discuss those effects here as well.

Rounding Modes[edit]

Rounding Errors[edit]

Relative Error[edit]

Relative error is one measure of error commonly used with floating point numbers. If \tilde x is an approximation to x, then the relative error, r, is defined as


  r = {{|x - \tilde x|} \over x}