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Issue No.02 - February (1998 vol.47)

pp: 152-161

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.663761

ABSTRACT

<p><b>Abstract</b>—A very-high radix digit-recurrence algorithm for the operation <tmath>$\sqrt {{x \mathord{\left/ {\vphantom {x d}} \right. \kern-\nulldelimiterspace} d}}$</tmath> 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 <tmath>$\sqrt {{x \mathord{\left/ {\vphantom {x d}} \right. \kern-\nulldelimiterspace} d}}$</tmath> 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.</p>

INDEX TERMS

Digit-recurrence algorithm, division, high-radix methods, inverse square-root, square-root.

CITATION

Tomás Lang, Elisardo Antelo, "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, February 1998, doi:10.1109/12.663761