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About 8,077 papers for “Multiplication algorithm”

Modified CMOS Multiplication Algorithm Using Optimized Array Structure

P. Assadee · Journal of Computers · 2009

In this paper, a new, high-speed multiplication algorithm using tree circuit and a novel inner product generator has been presented. In inner product generation step, a new Smith algorithm has been modified. In inner product reduction step, a new array structure has been proposed. In final addition step, a new algorithm has been used. In this work, improvements in multiplication algorithm by using a faster counter along the tree are presented. In this paper, the novel presented multiplication algorithm has been also analyzed in comparison with other multiplication algorithms. Based on the variation of inner product generator methods, a novel Smith algorithm is proposed. This work, presents a novel approach to reduce power of high-speed multiplication algorithm based on decreasing number of inner products. The reducing elements used into the multiplication algorithm architecture remove some inner product that have not effect in final addition. The proposed array structure and Smith algorithm has major effect in multiplication algorithm performance. Previous designs have been used to present a novel structure. A new multiplication algorithm is designed and simulated in 80 nm process. We used SPICE and some programming code for simulations. The latency has decreased by almost 15 percent and power consumption decreased by 14 percent. Our design reduced transistor count by 10 percent.

Cited by 0

Quantum Multiplication Algorithm Based on the Convolution Theorem

Mehdi Ramezani, Morteza Nikaeen, Farnaz Farman et al. · arXiv (Cornell University) · 2023

The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their theoretical limit and offer little room for further enhancement. However, with the advent of quantum computers and the need for quantum algorithms that can perform multiplication on quantum hardware, a new paradigm emerges. In this paper, inspired by convolution theorem and quantum amplitude amplification paradigm we propose a quantum algorithms for integer multiplication with time complexity $O(\sqrt{n}\log^2 n)$ which outperforms the best-known classical algorithm, the Harvey algorithm with time complexity of $O(n \log n)$. Unlike the Harvey algorithm, our algorithm does not have the restriction of being applicable solely to extremely large numbers, making it a versatile choice for a wide range of integer multiplication tasks. The paper also reviews the history and development of classical multiplication algorithms and motivates us to explore how quantum resources can provide new perspectives and possibilities for this fundamental problem.

Cited by 0Open access

Optimized Fast Scalar Multiplication Algorithm Based on DBNS

Xinchun Yin, Rong Zhao · 2009

Scalar multiplication is important in elliptic curve cryptography, the time that consumes is significant for it's applications. In this paper, the point arithmetic improved on elliptic curve over binary field such as 3P, 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> P, then proposed an optimized DBNS chain with loose constraint of exponents to short the chain's length. Combined the new DBNS chain and more efficient point arithmetic, introduced the optimized scalar multiplication algorithm. Experiments show that the new algorithm speed up scalar multiplication.

Cited by 1

Quantum multiplication algorithm based on the convolution theorem

Mehdi Ramezani, Morteza Nikaeen, Farnaz Farman et al. · Physical review. A/Physical review, A · 2023

The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their theoretical limit and offer little room for further enhancement. However, with the advent of quantum computers and the need for quantum algorithms that can perform multiplication on quantum hardware, a new paradigm emerges. In this paper, inspired by the convolution theorem and quantum amplitude amplification paradigm we propose a quantum algorithm for integer multiplication with time complexity of $O(\sqrt{n}{log}^{2}n)$ which outperforms the best-known classical algorithm, the Harvey algorithm with time complexity of $O(nlogn)$. Unlike the Harvey algorithm, our algorithm does not have the restriction of being applicable solely to extremely large numbers, making it a versatile choice for a wide range of integer multiplication tasks. The paper also reviews the history and development of classical multiplication algorithms and motivates us to explore how quantum resources can provide new perspectives and possibilities for this fundamental problem.

Cited by 7

Quantum algorithm for polynomial multiplication and its applications

Shang Gao, Rui‐Chen Huang, Bing‐Xin Liu et al. · EPJ Quantum Technology · 2025

Polynomial multiplication is a fundamental operation in various fields of science and engineering. This paper proposes a quantum algorithm for polynomial multiplication that achieves improved efficiency over classical approaches. The core innovation is the use of a quantum Fourier transform with digital encoding. The practical utility and versatility of this algorithm are highlighted through its application to several related computational problems, including string matching, Toeplitz matrix-vector multiplication, and matrix decomposition algorithm. Furthermore, an enhanced version of the quantum polynomial multiplication algorithm is introduced, offering improvements in both execution process and time complexity.

Cited by 0Open access

AN EFFICIENT PARALLEL ALGORITHM FOR MATRIX-VECTOR MULTIPLICATION

Bruce Hendrickson, ROBERT LELAND, Steven J. Plimpton · International Journal of High Speed Computing · 1995

The multiplication of a vector by a matrix is the kernel operation in many algorithms used in scientific computation. A fast and efficient parallel algorithm for this calculation is therefore desirable. This paper describes a parallel matrix-vector multiplication algorithm which is particularly well suited to dense matrices or matrices with an irregular sparsity pattern. Such matrices can arise from discretizing partial differential equations on irregular grids or from problems exhibiting nearly random connectivity between data structures. The communication cost of the algorithm is independent of the matrix sparsity pattern and is shown to scale as for an n×n matrix on p processors. The algorithm’s performance is demonstrated by using it within the well known NAS conjugate gradient benchmark. This resulted in the fastest run times achieved to date on both the 1024 node nCUBE 2 and the 128 node Intel iPSC/860. Additional improvements to the algorithm which are possible when integrating it with the conjugate gradient algorithm are also discussed.

Cited by 74

Investigation of the Performance of Nikhilam Multiplication Algorithm

Can Eyüpoğlu · Procedia - Social and Behavioral Sciences · 2015

Multiplication is one of the most important operations in computer arithmetic. Multiplication is used in many operations such as squaring, division and computing reciprocal. Moreover, multiplication is a very significant arithmetic operation for lots of signal processing applications which are convolution, correlation, frequency analysis, image processing etc. The efficiency of multiplication operation is crucial for the process time of these applications. Nikhilam algorithm is one of the algorithms developed for increasing the efficiency and reducing the cost in order to simplify multiplication. In this work, the performance of Nikhilam multiplication algorithm is analyzed in terms of the number of multiplication and the total process time for different bit lengths.

Cited by 6Open access

Communication-Optimal Parallel Algorithm for Strassen's Matrix Multiplication

Grey Ballard, James Demmel, Olga Holtz et al. · arXiv (Cornell University) · 2012

Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes communication. The algorithm outperforms all known parallel matrix multiplication algorithms, classical and Strassen-based, both asymptotically and in practice. A critical bottleneck in parallelizing Strassen's algorithm is the communication between the processors. Ballard, Demmel, Holtz, and Schwartz (SPAA'11) prove lower bounds on these communication costs, using expansion properties of the underlying computation graph. Our algorithm matches these lower bounds, and so is communication-optimal. It exhibits perfect strong scaling within the maximum possible range. Benchmarking our implementation on a Cray XT4, we obtain speedups over classical and Strassen-based algorithms ranging from 24% to 184% for a fixed matrix dimension n=94080, where the number of nodes ranges from 49 to 7203. Our parallelization approach generalizes to other fast matrix multiplication algorithms.

Cited by 9Open access

Floating Point Multiplication Based on Schonhage Strassen Algorithm

B. Srikanth, M. Siva Kumar, Kakarla Hari Kishore · International Journal of Engineering & Technology · 2018

In this paper, the single precision float point multiplication is performed using the Schonhage Strassen Algorithm. There are several types of floating point multiplications like Karatsubha and Toom cook. The Schonhage Strassen algorithm is conventionally a fixed point integer multiplication algorithm. The main advantage of the Schonhage Strassen multiplication is that, the multiplication of integer values greater than 5 digits ranging from 2215 to 2217 bit values proves to be efficient. The validation of the proposed floating point multiplication is done using FPGA real time implementation. The analysis of parameters like area and power are evaluated.

Cited by 3Open access

Dual-field Modular Multiplication Algorithm and Modular Inversion Algorithm with VLSI Implementation

Guanghua Chen, Jing-ming Zhu, Ming Liu et al. · JOURNAL OF ELECTRONICS INFORMATION TECHNOLOGY · 2010

有限域上的模乘和模逆运算是椭圆曲线密码体系的两个核心运算。该文在Blakley算法的基础上提出一种radix-4快速双有限域模乘算法，该算法采用Booth编码技术将原算法的迭代次数减少一半，并利用符号估计技术简化约减操作；在扩展Euclidean求逆算法的基础上提出一种能够同时支持双有限域运算的高效模逆算法，该算法不仅避免了大整数比较操作，而且提高了算法在每次迭代过程中的移位效率。然后针对这两种算法特点设计出一种能够同时完成双有限域上模乘和模逆操作的统一硬件结构。实现结果表明：256位的模乘和模逆统一硬件电路与同类型设计相比较，在电路面积没有增加的情况下，模乘运算速度提高68%，模逆运算的速度也提高了17.4%。

Cited by 3Open access

Analysis of different multiplication algorithm and FPGA implementation of recursive barrel shifter method for multiplication

Manoj M Kamble, Sunita P. Ugale · 2016

processing algorithm included multiplication as its processing heart. In case of signal and image processing, it mostly used functional unit. In this review paper we are introducing logically new, fast and more efficient multiplication algorithm that seem to fulfilled fast processing requirement. This paper introduces how effectively we can use barrel shifter for implementation of multiplication method. Further work will carried comparative study of different multiplier with respect to some parameters like cost, power consumption, area and speed. For implementation and parametric analysis, we are using XC3S400 FPGA hardware platform, VHDL coding language for hardware description. Xilinx ISE-simulation tool has many inbuilt compatible tools for parameter analysis like XPE for power estimation that we are using here. Paper comprises description of current scenario, existed multiplication methods and our proposed algorithm.

Cited by 0

Communication-Optimal Parallel Algorithm for Strassen's Matrix\n Multiplication

Grey Ballard, James Demmel, Olga Holtz et al. · arXiv (Cornell University) · 2012

Parallel matrix multiplication is one of the most studied fundamental\nproblems in distributed and high performance computing. We obtain a new\nparallel algorithm that is based on Strassen's fast matrix multiplication and\nminimizes communication. The algorithm outperforms all known parallel matrix\nmultiplication algorithms, classical and Strassen-based, both asymptotically\nand in practice.\n A critical bottleneck in parallelizing Strassen's algorithm is the\ncommunication between the processors. Ballard, Demmel, Holtz, and Schwartz\n(SPAA'11) prove lower bounds on these communication costs, using expansion\nproperties of the underlying computation graph. Our algorithm matches these\nlower bounds, and so is communication-optimal. It exhibits perfect strong\nscaling within the maximum possible range.\n Benchmarking our implementation on a Cray XT4, we obtain speedups over\nclassical and Strassen-based algorithms ranging from 24% to 184% for a fixed\nmatrix dimension n=94080, where the number of nodes ranges from 49 to 7203.\n Our parallelization approach generalizes to other fast matrix multiplication\nalgorithms.\n

Cited by 0Open access

Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm

Brice Boyer, Jean‐Guillaume Dumas, Clément Pernet et al. · arXiv (Cornell University) · 2007

We propose several new schedules for Strassen-Winograd's matrix multiplication algorithm, they reduce the extra memory allocation requirements by three different means: by introducing a few pre-additions, by overwriting the input matrices, or by using a first recursive level of classical multiplication. In particular, we show two fully in-place schedules: one having the same number of operations, if the input matrices can be overwritten; the other one, slightly increasing the constant of the leading term of the complexity, if the input matrices are read-only. Many of these schedules have been found by an implementation of an exhaustive search algorithm based on a pebble game.

Cited by 1Open access