The time complexity of Karatsuba algorithm for fast multiplication is O(nlog 3).ExampleIn the complete implementation of Karatsuba Algorithm, we are trying to multiply two higher-valued numbers. Here, since the long data type accepts decimals upto 18 places, we take the inputs as long values....
Three-term Karatsuba algorithmBit-parallel multiplierTrinomialsIn this paper, we continue the study of bit-parallel multiplier using three-term Karatsuba algorithm (KA), recently introduced by Li et al. (VLSI Design 2018). The three-term KA is the simplest variation of the classic Karatsuba ...
> implementing the Karatsuba algorithm, it is implementing the > schoolbook algorithm in two steps, by splitting the longer input into > two pieces. The surprising realization here is that there are actually (var1ndigits, var2ndigits) combinations where *only* doing mul_var_karatsuba_half() r...
any explicit multiplication, implementing the entire algorithm using solely addition. They require O(N) additions, each with bit-width of N. Thus, they have at least O(N 2 ) complexity where N is the bit-width of the computation. Such systems ...
10. The computer storage medium as recited in claim 1, wherein the product of the pair polynomials represents a product of a pair of large integers, and is utilized within a cryptographic algorithm. 11. A method comprising: identifying, by a computing system programmed with instructions configuri...
A fast algorithm of multiple-precisionmultiplicationbased on divide-and-conquer method; 一个基于分治法的快速多精度乘法 2. Calculate the value of determinant using matrix and themultiplicationof dividing matrix; 利用矩阵和分块矩阵的乘法计算行列式的值 ...
The proposed architecture can reduce the time x space complexity decreasing when the bit-size of multiplier is increasing.doi:10.1007/978-3-319-23207-2_22Shyan-Ming YuanChiou-Yng LeeChia-Chen FanSpringer International Publishing
We construct a bit-parallel multiplier for AOP based on a generalized Karatsuba algorithm.We examine the influence about multiplier efficiency with respect to decomposition of polynomial degree.The lower bound of the space complexity is m2/2+O(m{3/2})+O(m).The time complexity nearly matches ...
Meanwhile, its time complexity matches or is at most 1TX higher than the similar KA multipliers, where TX is the delay of one 2-input XOR gate. Index Terms Bit-parallel multiplier, n-Karatsuba algorithm, shifted polynomial basis, optimal, trinomials.Yin Li...
In this paper, we propose a Non-Redundant Karatsuba-Ofman algorithm (NRKOA) with removing redundancy operations, and design a parallel hardware architecture based on the proposed algorithm. Comparing with existing related Karatsuba architectures with the same time complexity, the proposed architecture ...