Lecture 2.
Floating point numbers
Anytime we use finite precision
arithmetic with floating point numbers we need to anticipate that the results
may not be identical to those obtainable by using infinite precision Real
arithmetic. Thus prior to looking at any numerical algorithms it is prudent to
get some understanding of what floating point numbers are and obtain some
insight as to how they behave.
I
breofly discussed binary floating point numbers. I then introduced the notion of
a floating point system and the
quantities realmax, realmin and eps. These quantities can be defined for any
floating point system. We worked out the values for the system F(10,3,-6,6).
I defined these concepts
today. My expectation is that after this morning's lecture people have a good
understanding of realmin and realmax. Furthermore, I think I made it clear that
eps and realmin are not the same in the floating point system
F(10,3,-6,6).
On Friday I will
continue with this talk and give general formulae for realmax, realmin, and eps
in terms of the parameters of a floating point system.
Posted: Thu - September 15, 2005 at 09:57 AM