
172 Chapter 5 Floating-point arithmetic
5.3 Floating-point operations
We now turn to consideration of arithmetic operations in floating-point systems, fol-
lowed by treatment of errors of such operations.
In Chapters 3 and 4 we established that the arithmetic in the subsets under D and
S and in all rows of Figure 1 can be defined by semimorphisms. We recall that if M
is any ringoid or vectoid and N M a symmetric lower or upper screen (or both) of
M , then a semimorphism
is defined by the following formulas:
(R1)
V
x2N
x D x,
(R2)
V
x,y2M
.x y ) x y/,
(R4)
V
x2M
.x/ D x,
(RG)
V
x,y2N
.x
ı
y :D .x ı y//,for ı2fC, , , =g with y 6D 0forıD=.
In general the operations ...