Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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02 Jul 2000
TL;DR: A “dissected” sieving algorithm which enumerates primes in the interval [x 1, x 2], using \(O(x_{2}^{1/3})\) bits of memory and using arithmetic operations on numbers of \(O(\rm ln \it x_{2}\) bits.
Abstract: We describe a “dissected” sieving algorithm which enumerates primes in the interval [x 1, x 2], using \(O(x_{2}^{1/3})\) bits of memory and using \(O(x_{2} -- x_{1} + x^{1/3}_{2}\) arithmetic operations on numbers of \(O(\rm ln \it x_{2})\) bits. This algorithm is based on a recent algorithm of Atkin and Bernstein [1], modified using ideas developed by Voronoi for analyzing the Dirichlet divisor problem [20]. We give timing results which show our algorithm has roughly the expected running time.
18 citations
TL;DR: In this article, the maximal energy of integral circulant graphs of prime power order ps and varying divisor sets was analyzed and the main result was that this maximal energy approximately lies between s(p-1)ps-1 and twice this value.
18 citations
TL;DR: In this paper, the authors present techniques for accelerating the floating-point computation of x/y when y is known before x. The goal is to get exactly the same result as with usual division with rounding to nearest.
Abstract: We present techniques for accelerating the floating-point computation of x/y when y is known before x. The proposed algorithms are oriented toward architectures with available fused-mac operations. The goal is to get exactly the same result as with usual division with rounding to nearest. It is known that the advanced computation of 1/y allows performing correctly rounded division in one multiplication plus two fused-macs. We show algorithms that reduce this latency to one multiplication and one fused-mac. This is achieved if a precision of at least n+1 bits is available, where n is the number of mantissa bits in the target format, or if y satisfies some properties that can be easily checked at compile-time. This requires a double-word approximation of 1/y (we also show how to get it). Compilers to accelerate some numerical programs without loss of accuracy can use these techniques.
18 citations
TL;DR: From this generalized equation, seven general HECDSA types are derived based on the efficiency requirements, and the securities of these general H OECD types are analyzed in detail.
18 citations
TL;DR: In this paper, it was shown that for a large class of stacks one typically encounters, this description does indeed characterize them and that each such stack can be described in terms of two simple procedures applied iteratively to its coarse space.
Abstract: In casual discussion, a stack is often described as a variety (the coarse space) together with stabilizer groups attached to some of its subvarieties. However, this description does not uniquely specify the stack. Our main result shows that for a large class of stacks one typically encounters, this description does indeed characterize them. Moreover, we prove that each such stack can be described in terms of two simple procedures applied iteratively to its coarse space: canonical stack constructions and root stack constructions.
More precisely, if $\mathcal X$ is a smooth separated tame Deligne-Mumford stack of finite type over a field $k$ with trivial generic stabilizer, it is completely determined by its coarse space $X$ and the ramification divisor (on $X$) of the coarse space morphism $\pi\colon \mathcal X \to X$. Therefore, to specify such a stack, it is enough to specify a variety and the orders of the stabilizers of codimension 1 points. The group structures, as well as the stabilizer groups of higher codimension points, are then determined.
18 citations