(1 +i) - ary GCD Computation inZ[ i ]as an Analogue to the Binary GCD Algorithm
نویسندگان
چکیده
منابع مشابه
Binary GCD algorithm
The binary GCD algorithm, also known as Stein’s algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein’s algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts, comparisons, and subtraction. Although the algorithm was first published by the Israeli physicist and programm...
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In this paper we analyze a slight modification of Jebelean’s version of the k-ary GCD algorithm. Jebelean had shown that on n-bit inputs, the algorithm runs in O(n) time. In this paper, we show that the average running time of our modified algorithm is O(n/ logn). This analysis involves exploring the behavior of spurious factors introduced during the main loop of the algorithm. We also introduc...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2000
ISSN: 0747-7171
DOI: 10.1006/jsco.2000.0422