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Karatsuba Square Root

Paul Zimmermann 1
1 POLKA - Polynomials, Combinatorics, Arithmetic
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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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Submitted on : Wednesday, May 24, 2006 - 11:05:58 AM
Last modification on : Friday, February 26, 2021 - 3:28:02 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:25:18 PM


  • HAL Id : inria-00072854, version 1



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



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