Abstract
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.
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CITATION STYLE
Bodrato, M., & Zanoni, A. (2012). A new algorithm for long integer cube computation with some insight into higher powers. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7442 LNCS, pp. 34–46). Springer Verlag. https://doi.org/10.1007/978-3-642-32973-9_4
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