A New Algorithm for Long Integer Cube Computation with Some Insight into Higher Powers
- Cite this paper as:
- Bodrato M., Zanoni A. (2012) A New Algorithm for Long Integer Cube Computation with Some Insight into Higher Powers. In: Gerdt V.P., Koepf W., Mayr E.W., Vorozhtsov E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg
A new approach for the computation of long integer cube (third power) based on a splitting-in-two divide et impera approach and on a modified Toom-Cook-3 unbalanced method is presented, showing that the “classical” square-and-multiply algorithm is not (always) optimal. The new algorithm is used as a new basic tool to improve long integer exponentiation: different techniques combining binary and ternary exponent expansion are shown. Effective implementations by using the GMP library are tested, and performance comparisons are presented.
AMS Subject Classification11N64 11A25 13B25
Keywords and phrasesToom-Cook cube third power long integers
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