Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Integer and polynomial multiplication: towards optimal toom-cook matrices
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
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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.