Hierarchical segmentation schemes for function evaluation
Hierarchical segmentation schemes for function evaluation
复制标题
功能评估的分层分割方案
DOI：
10.1109/fpt.2003.1275736
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
P. Cheung
中科院分区：
文献类型：
--
作者：
Dong;W. Luk;J. Villasenor;P. Cheung
本文提出了一种基于分段多项式近似和新颖的分层分割方案的函数评估方法。使用统一段和大小随二次方变化的段的新颖层次结构方案使我们能够特别好地逼近函数的非线性区域。这种划分是自动化的：针对给定函数、输入范围、多项式阶数、所需精度和有限精度约束生成有效的查找表及其系数。我们描述了一种算法来找到最佳的段数及其边界的位置，该算法用于分析函数的属性并确定方法的基准。我们的方法使用三个非线性复合函数 /spl Radic/-log(x)、x log(x) 和一个高阶有理函数来说明。我们给出了 8 到 24 位之间的各种操作数大小的一阶和二阶多项式近似的结果。
This paper presents a method for evaluating functions based on piecewise polynomial approximation with a novel hierarchical segmentation scheme. The use of a novel hierarchy scheme of uniform segments and segments with size varying by powers of two enables us to approximate non-linear regions of a function particularly well. This partitioning is automated: efficient look-up tables and their coefficients are generated for a given function, input range, order of the polynomials, desired accuracy and finite precision constraints. We describe an algorithm to find the optimum number of segments and the placement of their boundaries, which is used to analyze the properties of a function and to benchmark out approach. Our method is illustrated using three non-linear compound functions, /spl radic/-log(x), x log(x) and a high order rational function. We present results for various operand sizes between 8 and 24 bits for first and second order polynomial approximations.