Comparing several GCD algorithms
نویسنده
چکیده
0 binary, I-binary: The binary GCD algorithm ([lS]) and its improvement for multidigit integers (Gosper, see [12]). We compare the executron times of several algoixtliiiis for computing the G‘C‘U of arbitrary precasion iirlegers. These algorithms are the known ones (Euclidean, brnary, plus-mrnus), and the improved variants of these for multidigit compzltation (Lehmer and similar), as well as new algorithms introduced b y the author: an improved Lehmer algorithm using two digits in partial cosequence computation, and a generalization of the binary algorithm using a new concept of “m.0dalar conjugates”. The last two algorithms prove to be the fastest of all, giving a speed-,up of 6 to 8 times over th.e classical Euclidean scheme, and 2 times over the best currently known algorathins. Also, the generalized binary algorithm is suitable for systolic parallelization, an “least-significant digits first” pipelined manner.
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