β Scribed by Jeffrey Shallit; Jonathan Sorenson
No coin nor oath required. For personal study only.
We introduce a new left-shift binary algorithm, LSBGCD, for computing the greatest common divisor of two integers, and we provide an analysis of the worst-case behavior of this algorithm. The analysis depends on a theorem of Ramharter about the extremal behavior of certain continuants.
π SIMILAR VOLUMES
A simple shift algorithm is described enabling the exact determination of power functions and sample size distributions for a large variety of closed sequential two-sample designs with a binary outcome variable. The test statistics are assumed to be based on relative frequencies of successes or fail
The use of pairs of double digits in the Lehmer-Euclid multiprecision GCD algorithm halves the number of long multiplications, but a straightforward implementation of this idea does not give the desired speed-up. We show how to overcome the practical difficulties by using an enhanced condition for e