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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
586 CHAPTER IO Function Evaluation
,
[Initialize]
y[0] = 0; w[0] = 1 -x
[Recurrence]
forj =0...m
s j = SEL( w [j ]) ;
w[j + 1] +-- 2(wb]-sj
+sjw[j]2-J)
Yb + 1] ~
y[j]- L~
end for
[Result]
y[m 4-
1] ~,
ln(x)
where
9 The residual is in redundant form, represented by the pseudosum
WS
and
stored-carry
WC
bit-vectors. For simplicity, we use w[j] in the description.
9 m is the precision in bits.
9 SEL
is the continued-product digit selection function defined by
/ A
1 if w[j]>0
s j =SEL(w[j])
= 0 if-l_<w[j]_<0.25
-1 ifw[j]<-0.75
where w [j ] is an estimate of the residual w [j ] with t = 2 fractional bits.
9
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Publisher Resources

ISBN: 9781558607989