Multiplying Integers: On the Diverse Practices of Medieval Sanskrit Authors

More On Squaring and Multiplying Large Integers

t = vzge(b,w,a)

A quantum architecture for multiplying signed integers

Multiplying huge integers using Fourier transforms

Multiplying huge integers of n digits can be done in time O(n log(n)) using Fast Fourier Transforms (FFT), instead of the O(n) time complexity normally required. In this paper we present this technique from the viewpoint of polynomial multiplication, explaining a recursive divide-and-conquer approach to FFT multiplication. We have compared both methods of multiplication quantitatively and prese...

On the circuit complexity of the standard and the Karatsuba methods of multiplying integers

The goal of the present paper is to obtain accurate estimates for the complexity of two practical multiplication methods: standard (school) and Karatsuba [1]. Here, complexity is the minimal possible number of gates in a logic circuit implementing the required function over the basis {AND,OR,XOR,NAND,NOR,XNOR}. One can find upper estimates for the said methods e.g. in [2]. The standard method h...

survey on the rule of the due & hindering relying on the sheikh ansaris ideas

قاعده مقتضی و مانع در متون فقهی کم و بیش مستند احکام قرار گرفته و مورد مناقشه فقهاء و اصولیین می باشد و مشهور معتقند مقتضی و مانع، قاعده نیست بلکه یکی از مسائل ذیل استصحاب است لذا نگارنده بر آن شد تا پیرامون این قاعده پژوهش جامعی انجام دهد. به عقیده ما مقتضی دارای حیثیت مستقلی است و هر گاه می گوییم مقتضی احراز شد یعنی با ماهیت مستقل خودش محرز گشته و قطعا اقتضاء خود را خواهد داشت مانند نکاح که ...