航空发动机FADEC系统软件浮点数计算精度分析

航空发动机FADEC系统控制软件的计算精度和运行效率是一对不可缺少的特性.为提高航空发动机FADEC系统控制软件的浮点计算的计算精度和运行效率,从IEEE 754浮点数格式、浮点数的表示形式、浮点数四则运算的精度方面展开分析,并结合FADEC系统控制软件项目实际应用案例的数据结果,验证了精度分析结果的正确性,并以此为基础针对FADEC系统控制软件的浮点算法设计提出了设计准则,有助于提高控制软件的可靠性和安全性,可推广至其他行业的控制领域应用.     

编程语言中浮点数精度丢失问题

程序设计语言一般会出现浮点数精度丢失问题,这直接影响到程序执行结果的准确性和可靠性。以Java语言为例,从浮点数的存储结构上进行分析,找出了浮点数精度缺失问题产生的根源因素。为了解决此问题,Java语言提供了一个大数类BigDecimal,但是该类操作浮点数不方便,需要多次数据类型转换。提出了快捷的四舍五入解决方法,该方法同样适用于其他编程语言。     

浅析C语言程序设计中的浮点数

C语言作为一种高级程序设计语言,具有功能强大、程序设计灵活且支持底层应用等优点,因此广泛应用于科学计算、数据处理等领域.其中,浮点数的运算在计算机的CPU硬件到软件编译器、操作系统中均有所涉及.本文对C语言中的浮点数进行了较为详细的介绍.     

用scanf()函数输入浮点数出现问题的解决办法

本文讨论了用scanf()函数输入浮点数出现的问题,并分析了该问题产生的原因,最后文章重点给出了针对这类问题的4种解决方案.     

常用数据存储标准的一种研究方法

分析了数据的内部编码方式,详细讨论了单精度和双精度浮点数的内部编码标准,利用C语言教学中的共用体类型,提出了一种简单易行的研究内部编码的方法,即采用非常规方法引用C语言的共用体,从而获取数据的内部存储形式,通过实例对这一方法进行了详细说明.     

多小波阈值的遗传算法消噪变异

编码问题是遗传算法研究的难点。浮点数编码在函数和约束优化中明显优于其他编码,并能提高算法的局部搜索能力。浮点数编码在遗传环境中产生的噪音和对算法性能的影响,正在被研究者所关注。但目前尚无基于多小波阈值实现浮点数编码消噪变异的研究成果出现。首先研究了多小波和浮点数编码噪音的性质,提出了一种基于多小波阈值的浮点数编码消噪变异方法,并与其他算法进行比较实验。研究和实验结果表明,这种方法可明显提高算法的收敛精度和速度,改善算法的整体性能。     

非精确浮点数乘法器设计

随着电路系统数值运算范围以及数据运算精度的不断扩大,浮点数运算的研究变得越来越重要。但传统浮点数运算单元硬件复杂、功耗大、延时长,这些因素很大程度上制约着浮点数运算的性能。非精确计算可以减少容错设备的动态及静态能量损耗,作为解决以上问题的有效方法。提出了一种非精确浮点数乘法器的算法设计,同时将该算法应用于高动态范围图片的图像处理中,并将结果与精确浮点数乘法器的应用结果进行对比,结果表明所提出的非精确浮点数乘法器具有很好的性能。     

Delphi及Interbase浮点数运算的精度问题

在Ｄｅｌｐｈｉ中直接比较浮点数是否相等时出现问题。在Ｉｎｔｅｒｂａｓｅ中浮点数的运算存在较严重的精度问题。本文给出相应的解决办法。     

单精度浮点数累加和误差研究

计算机中进行浮点数加法运算时,需要进行对阶和右规格化操作,该操作会进行舍入处理,这种处理过程会产生误差,浮点数累加运算会造成误差的累积,导致计算结果精度不够甚至计算结果错误。通过实验手段研究单精度浮点数累加过程中不同结合顺序对浮点数累加和误差的影响,探索结合顺序导致计算误差的规律,为多核计算、GPU计算、多处理器计算等计算范型和计算结构提供选择结合方法的依据,便于发挥其并行计算的优势。     

浮点数的教学难点研究

本文归纳了浮点数教学过程中一些学生容易感到困惑的问题．针对浮点数不同格式的定义、规格化以及不同机器码表示时规格化浮点数的表示范围等问题进行了详细的分析。通过对学生理解上难点问题的分析总结,从而给浮点数教学理出一个清晰的思路。     

Incremental communication for multilayer neural networks

A new method of inter-neuron communication called incremental communication is presented. In the incremental communication method, instead of communicating the whole value of a variable, only the increment or decrement of its previous value is sent on a communication link. The incremental value may be either a fixed-point or a floating-point value. Multilayer feedforward network architecture is used to illustrate the effectiveness of the proposed communication scheme. The method is applied to three different learning problems and the effect of the precision of incremental input-output values of the neurons on the convergence behavior is examined. It is shown through simulation that for some problems even four-bit precision in fixed- and/or floating-point representations is sufficient for the network to converge. With 8-12 bit precisions almost the same results are obtained as that with the conventional communication using 32-bit precision. The proposed method of communication can lead to significant savings in the intercommunication cost for implementations of artificial neural networks on parallel computers as well as the interconnection cost of direct hardware realizations. The method can be incorporated into most of the current learning algorithms in which inter-neuron communications are required. Moreover, it can be used along with the other limited precision strategies for representation of variables suggested in literature.     

Least significant bit evaluation of arithmetic expressions in single-precision

Single-precision floatingpoint computations may yield an arbitrary false result due to cancellation and rounding errors. This is true even for very simple, structured arithmetic expressions such as Horner's scheme for polynomial evaluation. A simple procedure will be presented for fast calculation of the value of an arithmetic expression to least significant bit accuracy in single precision computation. For this purpose in addition to the floating-point arithmetic only a precise scalar product (cf. [2]) is required. If the initial floatingpoint approximation is not too bad, the computing time of the new algorithm is approximately the same as for usual floating-point computation. If not, the essential progress of the presented algorithm is that the inaccurate approximation is recognized and corrected. The algorithm achieves high accuracy, i.e. between the left and the right bound of the result there is at most one more floating-point number. A rigorous estimation of all rounding errors introduced by floating-point arithmetic is given for general triangular linear systems. The theorem is applied to the evaluation of arithmetic expressions.     

Numerical accuracy control in fixed-point arithmetic

The purpose of this paper is to look at the problem of propagation of round-off errors in fixed-point arithmetic and at various problems of checking solutions of equations already treated by La Porte and Vignes in the case of floating-point arithmetic. We first consider the probabilistic model for the numerical fixed-point representation on a computer, the evaluation of the mean value and of the standard deviation for the absolute error of the assignment operator A, and of elementary operators of arithmetic. We then compute the statistical estimate of the error in the computation of an inner product, and this leads us to the problem of checking the accuracy of the solution of linear systems and of algebraic equations.     

Fast transformation of three-dimensional graphics structures via mixed-point arithmetic

Real-time animation of three-dimensional structures on refreshed tube interactive graphics processors usually requires floating-point arithmetic hardware for matrix manipulation and object transformation by the resultant matrix. An algorithm is described which uses fixed-point hardware to effect the required transformations at speeds surpassing that possible with floating-point hardware with no effective loss in accuracy. The algorithm involves ‘mixed-point arithmetic’—limited precision floating-point multiplication, conversion to an integer-fraction doubleword, and fixed-point addition.     

快速成型中一种改进的轮廓线生成算法

在对STL模型分层求交线过程中,针对三角面片的边与切平面很接近时,浮点运算引起的精度损失可能导致的错误交线问题,提出一种基于STL模型局部拓扑的分层算法。将所有可能引起错误交线的三角面片提取出来,建立拓扑结构,以接近切平面的边在切平面的投影替代交线,消除了由于浮点运算误差导致的轮廓线缺边和重边的错误。实验结果表明,该算法在计算出交线段集后不需要再进行修复,简单连接后就能得出正确的切片轮廓线。     

基于深度神经网络的视频播放速度识别

针对目前的视频播放速度识别算法大多存在的提取精度差、模型参数量巨大的问题,提出了一种双支轻量化视频播放速度识别网络。首先,该网络是基于SlowFast双支网络架构组建的一个三维（3D）卷积网络;其次,为了弥补S3D-G网络在视频播放速度识别任务中存在的参数量大、浮点运算数多的缺陷,进行了轻量化的网络结构调整;最后,在网络结构中引入了高效通道注意力（ECA）模块,以通过通道注意力模块生成重点关注的内容对应的通道范围,这有助于提高视频特征提取的准确性。在Kinetics-400数据集上将所提网络与S3D-G、SlowFast网络进行对比实验。实验结果表明,所提网络在精确度差不多的情况下,模型大小和模型参数均比SlowFast减少了大约96%,浮点运算数减少到5.36 GFLOPs,显著提高了运行速度。     

数字地球渲染中单精度浮点数误差改正

目的 针对全球大场景渲染中单精度浮点数的低精度导致的图像抖动和撕裂问题,提出了一套完整的解决方法。方法 首先,使用全球四叉树结构来寻找新的坐标原点,避免了现有算法需要频繁切换世界坐标原点的缺点;其次,在新坐标系下进行坐标转换和矩阵转换,解决了像素坐标计算的误差导致的抖动问题;最后,在GPU中使用基于对数的深度计算方式来提高深度的分辨率,解决了深度计算误差导致的Z-Fighting现象。结果 实验结果表明所提方法能很好地解决单精度浮点导致的渲染问题。结论 此方法具有适应性强、实现复杂度低、精度和效率可控等优点。     

Low-Cost Microarchitectural Support for Improved Floating-Point Accuracy

Some processors designed for consumer applications, such as graphics processing units (CPUs) and the CELL processor, promise outstanding floating-point performance for scientific applications at commodity prices. However, IEEE single precision is the most precise floating-point data type these processors directly support in hardware. Pairs of native floating-point numbers can be used to represent a base result and a residual term to increase accuracy, but the resulting order of magnitude slowdown dramatically reduces the price/performance advantage of these systems. By adding a few simple microarchitectural features, acceptable accuracy can be obtained with relatively little performance penalty. To reduce the cost of native-pair arithmetic, a residual register is used to hold information that would normally have been discarded after each floating-point computation. The residual register dramatically simplifies the code, providing both lower latency and better instruction-level parallelism.     

Robust parallel computation in floating-point and SLI arithmetic

In this paper we consider the parallel computation of vector norms and inner products in floating-point and a proposed new form of computer arithmetic, the symmetric level-index system. The vector norms provide an illuminating example of the contrast between the two arithmetic systems under discussion in terms of the ability to program for (complete) robustness and parallelizability. The conflict between robustness of the computation—in the sense of the dual requirements of accuracy and freedom from overflow and underflow—and easy parallelization of the algorithms within a floating-point environment is made plain. It is seen that this conflict disappears if the symmetric level-index system of arithmetic is used. The freedom from overflow and underflow offered by this system allows the programming of the straightforward definitions in a way which is simple, robust and immediately parallelizable. Numerical results are given to illustrate the fact that the symmetric level-index system yields results of comparable accuracy to those of floating-point in cases where the latter system works and still yields results of high accuracy when the floating-point system fails altogether.