Depth-efficient threshold circuits for multiplication and symmetric function computation

Yeh, Chi‐Hsiang; Varvarigos, Emmanouel A.

doi:10.1007/3-540-61332-3_156

Cited by 4 publications

(1 citation statement)

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“…Prefix computation is also an important problem that appears often in arithmetic and algebraic computations [5]. There have been a very large number of papers investigating fast and/or cost-effective solutions to these problems [1,2,4,6,7,8,9,10,13,14,15,16,17]. In this paper, we propose efficient circuits to perform prefix computation and addition.…”

Section: Introductionmentioning

confidence: 99%

Optimal-depth circuits for prefix computation and addition

Yeh

Varvarigos²,

Parhami³

Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154)

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Addition and prefix computation are among the most fundamental problems in arithmetic and algebraic computation. In this paper, we present efficient circuits for performing prefix computation and addition with small depth and size and flexible fan-in (i.e., the maximum fan-in can be selected as a small constant or a larger constant/nonconstant number). In particular, we show that any prefix operation of n inputs can be computed using a circuit of fan-in k, depth logkn + o(logkn) + O(1), gate complexity O(n), and edge d-I complexity O(n log* *"" * n), for any constant integer d. We show that the sum of two n-bit numbers can be found using an AND-OR circuit of fan-in k, depth logkn + o(logkn) + d-I O(1), and edge complexity O(n(log** ""*n)2), for any constant integer d. In particular, the depths of our circuits for prefix computation and addition are optimal within a factorofl + o(1), for any fan-in k = n °(l).

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