Composite Iterative Algorithm and Architecture for q-th Root Calculation

Alvaro Vazquez 1 Javier Bruguera 2
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : An algorithm for the q-th root extraction, being q any integer, is presented in this paper. The algorithm is based on an optimized implementation of X^{1/q} by a sequence of parallel and/or overlapped operations: (1) reciprocal, (2) digit-recurrence logarithm, (3) left-to-right carry-free multiplication and (4) on-line exponential. A detailed error analysis and two architectures are proposed, for low precision q and for higher precision q. The execution time and hardware requirements are estimated for single and double precision floating-point computations for several radices; this helps to determine which radices result in the most efficient implementations. The architectures proposed improve the features of other architectures for q-th root extraction.
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Alvaro Vazquez, Javier Bruguera. Composite Iterative Algorithm and Architecture for q-th Root Calculation. [Research Report] RR-7564, INRIA. 2011, pp.30. ⟨inria-00575573⟩

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