Energy-Efficient VLSI Realization of Binary64 Division With Redundant Number Systems

Amanollahi, Saba; Jaberipur, Ghassem

doi:10.1109/tvlsi.2016.2604346

Cited by 7 publications

(1 citation statement)

References 15 publications

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“…Interest in the acceleration of arithmetic circuits using redundant number systems is growing. Signed-digit representations have been used within high-radix adders [10] and dividers [11], and constant-vector multipliers [12], to improve performance and reduce power consumption versus their conventional equivalents. Fast multipliers using signed-digit representation during their partial product generation [13] and reduction [14] steps have also been proposed.…”

Section: Hardware Applications Of Redundancymentioning

confidence: 99%

Digit Stability Inference for Iterative Methods Using Redundant Number Representation

McInerney

Davis

et al. 2021

IEEE Trans. Comput.

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In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under-or over-budgeted for the solution of the problem at hand. Significant proportions of these performance improvements stem from the ability to infer the existence of identical most-significant digits between iterations. This technique uses properties of algorithms operating on redundantly represented numbers to allow the generation of those digits to be skipped, increasing efficiency. It is unable, however, to guarantee that digits will stabilize, i.e., never change in any future iteration. In this article, we address this shortcoming, using interval and forward error analyses to prove that digits of high significance will become stable when computing the approximants of systems of linear equations using stationary iterative methods. We formalize the relationship between matrix conditioning and the rate of growth in most-significant digit stability, using this information to converge to our desired results more quickly. Versus our previous work, an exemplary hardware realization of this new technique achieves an up-to 2.2× speedup in the solution of a set of variously conditioned systems using the Jacobi method.

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