We present three parallel implementations of the Karatsuba algorithm for long integer multiplication on a distributed memory architecture and discuss the experimental results obtained on a Paragon computer. The first two implementations have both time complexity O ( n ) on n log 2 3 processors, but...
A series of programs that enable one's investigations in the algebraic complexity theory such as matrix multiplication algorithms, primality tests, algebraic complexity, sorting algorithms etc. Each algorithm is accompanied by a comparative time complexity analysis and a class of test cases and test su...
The CIOS method of Montgomery algorithm is improved via the idea ofKaratsuba-Ofman algorithm,: the decrease rate amounts to nearly 25%. 利用Karatsuba-Ofman算法的思想,改进了Montgomery模乘的CIOS实现算法:一方面,改进后的CIOS算法在时间效率上有较大提高,减少的乘法次数比率接近25%;另一方面,改进后的算法...
Specifically, we found that related Mastrovito matrix is very simple for equally spaced trinomial (EST) combined with classic Karatsuba algorithm (KA), which leads to a highly efficient Karatsuba multiplier. In this paper, we consider a new special class of irreducible trinomial, namely, xm+xm/...
* var1 with each slice one at a time. As a result, the recursive call to * mul_var() will have balanced inputs, which improves the performance of * divide-and-conquer algorithm, such as the Karatsuba. */ static void mul_var_lopsided(const NumericVar *var1, const NumericVar *var2...
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 ...
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...
A target value is found by performing an NRHKOA(Non-Redundant Half Karatusba-Ofman Algorithm) after finding the sum. Output is found by replacing the inputted value with the target value and recursively repeating steps from the second step.LIM, JONG IN...
In this paper, we improve the Preprocess-then-NTT technique by mixing it with Karatsuba multiplication such that the time complexity is better than the original NTT algorithm asymptotically. The claim was also verified in our experiments. As a result, our new algorithm not only relaxes the ...
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 ...