Table 3 Overlapping intervals and criteria.

From: Radix-4 CORDIC algorithm based low-latency and hardware efficient VLSI architecture for Nth root and Nth power computations

Selection function (\(\sigma _j\))

Criteria

Overlapping intervals

2

\(W^j\ge 1.5*X^j\)

\(\left[ \frac{4}{3}X^j,\frac{5}{3}X^j\ \right]\)

1

\(1.5*X^j\ge W^j\ge 0.5*X^j\)

\(\left[ \frac{1}{3}X^j,\frac{2}{3}X^j\ \right]\)

0

\({0.5*X^j\ge W}^j\ge -0.5*X^j\)

\(\left[ -\frac{2}{3}X^j,-\frac{1}{3}X^j\ \right]\)

-1

\({-0.5*X^j\ge W}^j\ge -1.5*X^j\)

\(\left[ -\frac{5}{3}X^j,-\frac{4}{3}X^j\ \right]\)

-2

\({-1.5*X^j\ge W}^j\)

\(\left[ -\frac{8}{3}X^j,-\frac{7}{3}X^j\ \right]\)

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