
Linear Convergence Method 581
Selection by Rounding for (Very) High Radices
Convergence to 1 permits selection by rounding and therefore a high-radix al-
gorithm. However, in the first iterations selection by rounding is not possible, so
that an initial approximation of 1/x by other means is required. This can be done
by table lookup or by a linear approximation (see Section 7.1.3).
In selection by rounding, the digit is obtained by rounding the carry-save
residual (truncated to fractional bit t). Calling this truncated residual G[j ], we
get
The next residual is then
Since
L lj
ss-
U]+j
( L 1j )
w[j+l]--r w[j]-