Floating Point/Rounding

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.

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

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