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  • 1998
  • Issue No. 2 - February
  • Abstract - 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
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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
February 1998 (vol. 47 no. 2)
pp. 152-161

Abstract—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.

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Index Terms:
Digit-recurrence algorithm, division, high-radix methods, inverse square-root, square-root.
Citation:
Elisardo Antelo, Tomás Lang, Javier D. Bruguera, "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," IEEE Transactions on Computers, vol. 47, no. 2, pp. 152-161, Feb. 1998, doi:10.1109/12.663761
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