基于FPGA的开方运算实现

开方运算作为数字信号处理(DSP)领域内的一种基本运算,其基于现场可编程门列阵(FPGA)的工程实现具有较高的难度.本文分析比较了实现开方运算的牛顿-莱福森算法、逐次逼近算法、非冗余开方算法3种算法,并给出了基于FPGA的开方器的实现方法,同时对逐次逼近算法、非冗余开方算法和IP_core的性价比进行了分析比较.     

浮点开方运算单元的电路设计

文章提出了一种基于逐位循环开方算法,"四位一开方"的浮点开方运算单元的电路设计方案,使限制周期时间的循环迭代部分的门级数降低到14级。按14级门延时为周期时间计算,完成一个IEEE单、双精度浮点数的开方运算分别需要15和29周期。同时,文章对目前开方运算所采用的两类主要的算法-逐位循环开方算法和牛顿－莱福森迭代开方算法进行了描述,其中包括数的冗余表示等内容。     

新型的快速高准确度开方算法及程序设计

介绍一种新型的快速高准确度开方算法，特别适用于需要用计算机进行ａ２＋ｂ２型式开方运算场合。算法巧妙地将开方变量由两个减少为一个，将变量变化区间由整个实数轴缩小为［０，１］区间，进而采用查表与插值相结合的方法，实现了高准确度、快速开方运算。在单片机８０ｃ１９６ｋｂ上，利用ＰＬ／Ｍ９６语言编程进行了运算，效果良好。     

一种单精度浮点倒数开方运算的硬件实现

单精度浮点倒数开方运算在GPU设计中经常会用到。实现这种运算一般有两种方法,迭代法和查表法。迭代法要根据精度要求确定迭代次数,只需要很小的存储器保存迭代初值,但需要的运算器数量较多。查表法根据输入的数据直接从ROM中查表得到结果,需要占用的存储资源比较多。该文提出了一种间接查表法实现的浮点倒数开方运算实现方法,将迭代法和直接查表法的优点结合起来。经过理论推导和硬件仿真验证,该算法能够满足单精度浮点数的运算精度。     

快速开方算法在微控制器上的实现

本文介绍了两种微控制器快速开方算法:改进牛顿-拉夫逊算法和模拟手算开方算法。前者是以牛顿-拉夫逊算法为基础的一种改进算法;后者是模拟手算开方过程实现开方的微控制器算法,这两种算法都具有较高的开方速度和计算精度。文章中作者以32位数开方为例,详细的介绍了这两种算法用汇编语言实现的过程,并给出算法实现的流程图,最后根据两种算法的特点和实际运算时间,总结了两种算法的优缺点。     

快速开方算法在微控制器上的实现

介绍了两种微控制器快速开方算法:改进牛顿-拉夫逊算法和模拟手算开方算法。前者是以牛顿-拉夫逊算法为基础的一种改进算法;后者是模拟手算开方过程实现开方的微控制器算法,这两种算法都具有较高的开方速度和计算精度。笔者以32位数开方为例,详细介绍了这两种算法用汇编语言实现的过程,并给出算法实现的流程图,最后根据两种算法的特点和实际运算时间,总结了两种算法的优缺点。     

硬件实现开方算法

开方是一个常用的初等函数。机器实现开方运算,一般用子程序,也有用硬件实现的,如科学院计算所的013机,复旦大学的FD-753机等。实际上,开方运算作为除法运算的一个特例,可构成一套和除法算法平行的算法。执行一次开方时间和它相应的除法算法的时间是一样的,而增加的硬件又是非常有限。这样做可以大大提高开方运算的执行时间。据753机统计,效率可提高一个数量级。又可以节省一些内存单元。因此,用硬件实现开方运算。对于大型通用计算机来说是非常必要而又很合理的。     

快速开方算法在微控制器上的实现

介绍了两种微控制器快速开方算法：改进牛顿-拉夫逊算法和模拟手算开方算法。前者是以牛顿-拉夫逊算法为基础的一种改进算法；后者是模拟手算开方过程实现开方的微控制器算法，这两种算法都具有较高的开方速度和计算精度。笔者以32位数开方为例，详细介绍了这两种算法用汇编语言实现的过程，并给出算法实现的流程图，最后根据两种算法的特点和实际运算时间，总结了两种算法的优缺点。     

Z80二进制开方运算程序

本文根据文献[1]给出的算法,用Z80汇编语言设计了二进制开方运算程序。文献[1]给出的是一种新颖的二进制开方算法,它比文献[2]给出的各种开方算法简单、直观。此算法只需进行数的大小比较和减法,无须进行修正系数,可很方便地在廉价的微处理器上用程序实现,其精度可达任意位。此算法由下式给出     

基于浮点数的Cholesky分解FPGA实现

在阵列信号抗干扰算法中,常常需要求解协方差矩阵的逆矩阵。Cholesky分解利用了协方差矩阵的厄米特（Hermitian）正定的特性,大大简化了矩阵求逆运算的计算量。论文介绍了Cholesky分解数学原理,并提出了一种适合FPGA实现的结构。基于浮点数的算法实现相比传统的定点数,大大提高了结果的精度。由于Cholesky分解需要涉及浮点数的开方运算,论文引入了平方根倒数法来提高开方运算的速度。通过仿真与实测,选取了最优的资源与速度的实现方案。     

短波信道平方根卡尔曼自适应均衡算法研究

针对短波突发通信的特点,基于判决反馈均衡器,研究平方根卡尔曼自适应均衡算法。该算法的参数选取对均衡的收敛速率和信道的衰落速率敏感,探究一种改进的平方根卡尔曼算法,运用Matlab工具对2种算法的性能进行仿真比较。仿真结果表明,在短波信道下,改进算法克服了原算法的缺点,具有很好的稳定性,并且不会牺牲收敛速率,其性能优于平方根卡尔曼算法。     

根生群优化算法

针对全局优化问题,基于一类支持向量数据描述（SVDD）和已有的根系生长算法提出一种新的智能优化算法——根生群优化算法,将根系划分为主根群体和侧根群体。基于SVDD描述主根群体的生长行为,将土壤中养分浓度最高的位置作为全局优化的目标,构建了根系生长模型;分析了RGSO的数学模型,从理论上证明了RGSO的收敛性。在实验中,与当前最先进的其他三个算法进行综合比较,并观察了不同参数对优化效果的影响。实验结果验证了RGSO的收敛性和有效性,表明RGSO是一种解决全局优化问题的有效算法。     

Eigenfactor solution of the matrix Riccati equation--A continuous square root algorithm

This paper introduces a new algorithm for solving the matrix Riccati equation. Differential equations for the eigenvalues and eigenvectors of the solution matrix are developed in which their derivatives are expressed in terms of the eigenvalues and eigenvectors themselves and not as functions of the solution matrix. The solution of these equations yields, then, the time behavior of the eigenvalues and eigenvectors of the solution matrix. A reconstruction of the matrix itself at any desired time is immediately obtained through a trivial similarity transformation. This algorithm serves two purposes. First, being a square root solution, it entails all the advantages of square root algorithms such as nonnegative definiteness and accuracy. Secondly, it furnishes the eigenvalues and eigenvectors of the solution matrix continuously without resorting to the complicated route of solving the equation directly and then decomposing the solution matrix into its eigenvalues and eigenvectors. The algorithm which handles cases of distinct as well as multiple eigenvalues is tested on several examples. Through these examples it is seen that the algorithm is indeed more accurate than the ordinary one. Moreover, it is seen that the algorithm works in cases where the ordinary algorithm fails and even in cases where the closed-form solution cannot be computed as a result of numerical difficulties.     

室内环境下同步定位与地图创建改进算法

提出了一种室内环境下基于平方根无迹卡尔曼滤波（SRUKF）的同步定位与地图创建（SLAM）算法． 该方法在每步迭代中采用平方根无迹粒子滤波器进行机器人状态估计,并引入平方根无迹卡尔曼滤波器定位路标, 进而完成机器人状态和相应路标信息更新．将本文算法与机器人运动模型和红外标签观测模型结合进行了仿真和实 验,结果表明,本算法在同步定位和地图创建过程中提高了机器人状态和路标估计的精度及稳定性．     

Characterization of robust root loci of polytopes of polynomials

This paper deals with the robust root locus problem of a polytope of real polynomials. First, a simple and efficient algorithm is presented for testing if the value set of a polytopic family of polynomials includes the origin of the complex plane. This zero-inclusion test algorithm is then applied along with a pivoting procedure to construct the smallest set of regions in the complex plane which characterizes the robust root loci of a polytope of polynomials.     

Measurement updating using the U-D factorization

The discrete linear filtering problem is treated by factoring the filter error covariance matrix as P = UDU^T. Efficient and stable measurement updating recursions are developed for the unit upper triangular factor, U, and the diagonal factor, D. This paper treats only the parameter estimation problem; effects of mapping, inclusion of process noise and other aspects of filtering are treated in separate publications. The algorithm is simple and, except for the fact that square roots are not involved, can be likened to square root filtering. Like the square root filter our algorithm guarantees nonnegativity of the computed covariance matrix. As is the case with the Kalman filter, our algorithm is well suited for use in real time. Attributes of our factorization update include: efficient one point at a time processing that requires little more computation than does the optimal but numerically unstable conventional Kalman measurement update algorithm; stability that compares with the square root filter and the variable dimension flexibility that is enjoyed by the square root information filter. These properties are the subject of this paper.     

32位嵌入式系统中扩展精度数学算法实现

提出了一种32位嵌入式系统中应用的扩展精度数学算法。适用于缺乏数字协处理器硬件支持并且软件浮点运算达不到系统时间要求的系统。算法运算数据精度高、扩展性好。介绍了32位乘法、除法、开方算法以及64位加法、减法、乘法算法。     

Root growth model: a novel approach to numerical function optimization and simulation of plant root system

This paper presents a general optimization model gleaned ideas from root growth behaviours in the soil. The purpose of the study is to investigate a novel biologically inspired methodology for complex system modelling and computation, particularly for optimization of higher-dimensional numerical function. For this study, a mathematical framework and architecture are designed to model root growth patterns of plant. Under this architecture, the interactions between the soil and root growth are investigated. A novel approach called “root growth algorithm” (RGA) is derived in the framework and simulation studies are undertaken to evaluate this algorithm. The simulation results show that the proposed model can reflect the root growth behaviours of plant in the soil and the numerical results also demonstrate RGA is a powerful search and optimization technique for higher-dimensional numerical function optimization.     

基于定点DSP的浮点开平方算法的实现

本文提出了基于TMS320C2XX定点DSP的浮点开平方算法，给出了实现方法及程序清单，实践证明该方法具有精度高，运算速度快、程序简单等特点。