Lecture 3.
Realmax, realmin, and
eps.
Today we continued with our exploration
of floating point systems. Using a running example to assist us, we obtained
expressions for realmax, realmin, and eps, using the parameters defining the
floating point system. We saw that the sizes of realmax and realmin are related
to the size of the exponent, and the size of eps is related to the size of the
mantissa.
Roundoff errors are
introduced by using floating point arithmetic. When a number is greater than
floating point realmax it causes
overflow.
A number less than realmin causes
underflow.
The relative
roundoff error, that is, the distance
between a floating point number and the Real value it represents, is eps when
chopping, or eps/2 when rounding.
Posted: Fri - September 16, 2005 at 08:48 AM