A hardware algorithm for fast logarithmic computation with exponential convergence rate

Abstract

A hardware algorithm is proposed for improving the speed of the linear digit‐recurrence logarithmic algorithm. The convergence rate of this logarithmic algorithm is exponential. Furthermore, the size of the lookup tables used in the algorithm is smaller than the size of the lookup tables used in the digit‐recurrence algorithms. When the word length of the operand is less than or equal to 64 bits, the operations involved in each stage of the logarithmic computation only include small table lookup operation, digit‐multiplication, and simple square operations. We conclude that the hardware implementation of our proposed algorithm is very efficient.     

The computation of the exponential and logarithmic mappings and their first and second linearizations

We describe two simple methods for the evaluation of the exponential and logarithmic mappings and their first and second linearizations based on the Taylor expansion and the spectral representation. We also provide guidelines for switching between those representations on the basis of the size of the argument. The first and second linearizations of the exponential and logarithmic mappings provided here are based directly on the exponential formula for the solutions of systems of linear ordinary differential equations. This representation does not require the use of perturbation formulae for eigenvalues and eigenvectors. Our approach leads to workable and straightforward expressions for the first and second linearizations of the exponential and logarithmic mappings regardless of degeneracies in the spectral decomposition of the argument. Copyright © 2001 John Wiley & Sons, Ltd.     

Multiquadric and its shape parameter—A numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation

Hardy’s multiquadric and its related interpolators have been found to be highly efficient for interpolating continuous, multivariate functions, as well as for the solution of partial differential equations. Particularly, the interpolation error can be dramatically reduced by varying the shape parameter to make the interpolator optimally flat. This improvement of accuracy is accomplished without reducing the fill distance of collocation points, that is, without the increase of computational cost. There exist a number of mathematical theories investigating the multiquadric family of radial basis functions. These theories are often not fully tested due to the computation difficulty associated with the ill-conditioning of the interpolation matrix. This paper overcomes this difficulty by utilizing arbitrary precision arithmetic in the computation. The issues investigated include conditional positive definiteness, error estimate, optimal shape parameter, traditional and effective condition numbers, round-off error, derivatives of interpolator, and the edge effect of interpolation.     

基于生物发光的高灵敏度ATP自动测试系统研究

针对高灵敏度、宽响应范围及自动检测三磷酸腺苷(ATP)的需求,设计了一种基于生物发光原理的ATP检测系统.系统采用自动加样技术,在发光反应的同时开始记录光强,使仪表检测自动化,且提高检测灵敏度;在优化光电检测单元设计和减小杂散光及电磁干扰的同时,提高荧光检测效率;通过电路和数据处理算法优化提高仪表检测范围.以浓度为10-15～10-6 M范围内的标准ATP溶液进行了实验,结果表明仪表测量光强与ATP实际浓度相关系数为0.974,检测范围达9个数量级.与市场相关仪器相比,该系统具有自动化测试,性能和灵敏度高、响应范围宽的特点,在ATP测量以及相关领域如细菌测量、毒性测试及卫生状况检测等方面具有广泛的应用前景.     

Non-binary decomposition trees—a method of reliability computation for systems with known minimal paths/cuts

A coherent system with independent components and known minimal paths (cuts) is considered. In order to compute its reliability, a tree structure T is constructed whose nodes contain the modified minimal paths (cuts) and numerical values. The value of a non-leaf node is a function of its child nodes' values. The values of leaf nodes are calculated from a simple formula. The value of the root node is the system's failure probability (reliability). Subsequently, an algorithm computing the system's failure probability (reliability) is constructed. The algorithm scans all nodes of T using a stack structure for this purpose. The nodes of T are alternately put on and removed from the stack, their data being modified in the process. Once the algorithm has terminated, the stack contains only the final modification of the root node of T, and its value is equal to the system's failure probability (reliability).     

一种低成本高性能的巡逻保安机器人

为满足在办公室、仓库等建筑内巡逻的要求,研制了一种低成本、高性能的巡逻保安机器人.其传感器系统采用分层模糊理论,能够在比较复杂的情况下完成自主导航和障碍避碰等任务.火灾探测系统采用神经网络和灰色预测理论,提高了报警的灵敏度,减少了误报警,缩短了报警时间.无线通讯的方式更适合于网络监控和远程操纵.实验证明,该巡逻保安机器人具有低成本、高性能的特点,具有较高的性价比,适合办公室、仓库、厂房等环境的巡逻与监控.