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arxiv: 1207.4497 · v1 · pith:DRNDPHYQnew · submitted 2012-07-18 · 💻 cs.DS · math.CO

Efficient Algorithms for Zeckendorf Arithmetic

Connor Ahlbach , Jeremy Usatine , Nicholas Pippenger This is my paper
classification 💻 cs.DS math.CO
keywords linearperformedzeckendorfadditionalgorithmsarithmeticcombinationaldepth
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We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be performed by combinational logic networks with linear size and logarithmic depth. The implications of these results for multiplication, division and square-root extraction are also discussed.

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