Computation of $\sqrt {{x \mathord{\left/ {\vphantom {x d}} \right. \kern-\nulldelimiterspace} d}}$ in a Very High Radix Combined Division/Square-Root Unit with Scaling and Selection by Rounding

• Authors: Elisardo Antelo;Tomás Lang;Javier D. Bruguera
• Venue: IEEE Transactions on Computers
• Year: 1998

A very-high radix digit-recurrence algorithm for the operation $\sqrt {{x \mathord{\left/ {\vphantom {x d}} \right. \kern-\nulldelimiterspace} d}}$ is developed, with residual scaling and digit selection by rounding. This is an extension of the division and square-root algorithms presented previously, and for which a combined unit was shown to provide a fast execution of these operations. The architecture of a combined unit to execute division, square-root, and $\sqrt {{x \mathord{\left/ {\vphantom {x d}} \right. \kern-\nulldelimiterspace} d}}$ is described, with inverse square-root as a special case. A comparison with the corresponding combined division and square-root unit shows a similar cycle time and an increase of one cycle for the extended operation with respect to square-root. To obtain an exactly rounded result for the extended operation a datapath of about 2n bits is needed. An alternative is proposed which requires approximately the same width as for square-root, but produces a result with an error of less than one ulp. The area increase with respect to the division and square root unit should be no greater than 15 percent. Consequently, whenever a very high radix unit for division and square-root seems suitable, it might be profitable to implement the extended unit instead.