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Reports (Research Report) Year : 1999

Karatsuba Square Root

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Abstract

We exhibit an algorithm to compute the square-root with remainder of a n-word number in 3\2word operations, where K(n) is the number of words operations to multiply two n-word numbers using Karatsuba's algorithm. If the remainder is not needed, the cost can be reduced to K(n) on average. This algorithm can be used for floating-point or polynomial computations too; although not optimal asymptotically, its simplicity gives a wide range of use, from about 50 to 1,000,000 digits, as shown by computer experiments.
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Dates and versions

inria-00072854 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00072854 , version 1

Cite

Paul Zimmermann. Karatsuba Square Root. [Research Report] RR-3805, INRIA. 1999, pp.8. ⟨inria-00072854⟩
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