COMPUTATION OF ROOT-X D IN A VERY HIGH RADIX COMBINED DIVISION/SQUARE-ROOT UNIT WITH SCALING AND SELECTION BY ROUNDING/

A very-high radix digit-recurrence algorithm for the operation root s/ d is developed, with residual scaling and digit selection by rounding. This is an extension of the division and square-root algorithms prese nted previously, and for which a combined unit was shown to provide a fast execution of these operations. The architecture of a combined uni t to execute division, square-root, and root x/d is described, with in verse square-root as a special case. A comparison with the correspondi ng combined division and square-root unit shows a similar cycle time a nd an increase of one cycle for the extended operation with respect to square-root. To obtain an exactly rounded result for the extended ope ration a datapath of about 2n bits is needed. An alternative is propos ed which requires approximately the same width as for square-root, but produces a result with an error of less than one ulp. The area increa se with respect to the division and square root unit should be no grea ter than 15 percent. Consequently, whenever a Very high radix unit for division and square-root seems suitable, it might be profitable to im plement the extended unit instead.