Correct rounding of values to the nearest representable value avoids systematic

*biases*in calculations and slows the growth of errors. Rounding ties to even removes the*statistical**bias*that can occur in adding similar figures. Directed rounding was intended as an aid with checking error bounds, for instance in interval arithmetic. It is also used in the implementation of some functions. The mathematical basis of the operations enabled high precision multiword arithmetic subroutines to be built relatively easily. The single and double precision formats were designed to be easy to sort without using floating-point hardware.