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Digital Arithmetic
book

Digital Arithmetic

by Miloš D. Ercegovac, Tomás Lang
September 2003
Intermediate to advanced content levelIntermediate to advanced
709 pages
26h 51m
English
Morgan Kaufmann
Content preview from Digital Arithmetic
Floating-Point Division and Square Root
461
8~176
......... qqqqqqqq .........
I I I I
qT
q c yyyyyyyyyyyyyyyyyyyyyyy
qt A B C
rt + + -
F
I a U R m 8.28
Two-sided quotient approximation.
For a two-sided approximation,
]q - qc
] < 2-(f+1) 8.92
The situation is described by Figure 8.28.
As can be seen,
qt
can take three possible values. So,
rt -- x - qtd
is com-
puted and
qT --qt
if0 <
rt
< 2-(f+l)d
qT --qt +
2-(f+l)
if rt >
2-(f+l)d
qT -- qt --
2-(f+l)
if rt < 0
This requires a comparison
ofrt
with 2-(f+l)d. A variation does not require this
comparison, but an approximation with an error of less than 2 -(f+2), that ...
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Publisher Resources

ISBN: 9781558607989