Numeric function generators using piecewise arithmetic expressions
Numeric function generators using piecewise arithmetic expressions
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使用分段算术表达式的数值函数生成器
DOI：
10.1109/ismvl.2011.32
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Jon Butler
中科院分区：
文献类型：
--
作者：
Shinobu Nagayama;Tsutomu Sasao;Jon Butler
提出了一种新的基于分段算术表达式的数值函数发生器结构。所提出的架构是可编程的，他们实现了广泛的数字功能。为了为给定函数设计NFG，我们将函数的域划分为均匀的段，并将每个段中的子函数转换为算术谱。从这个算术谱出发，我们推导出一个算术表达式，并用硬件实现了这个算术表达式。由于算术谱具有许多零系数和重复系数，因此通过在表中仅存储不同的非零系数，我们可以显着减少存储算术系数所需的表大小。实验结果表明，表的大小可以减少到只有一个小的百分比所需的表存储所有的算术系数。我们还提出了技术，以减少表的大小进一步提高性能。
This paper proposes new architectures for numeric function generators (NFGs) using piecewise arithmetic expressions. The proposed architectures are programmable, and they realize a wide range of numeric functions. To design an NFG for a given function, we partition the domain of the function into uniform segments, and transform a sub-function in each segment into an arithmetic spectrum. From this arithmetic spectrum, we derive an arithmetic expression, and realize the arithmetic expression with hardware. Since the arithmetic spectrum has many zero coefficients and repeated coefficients, by storing only distinct nonzero coefficients in a table, we can significantly reduce the table size needed to store arithmetic coefficients. Experimental results show that the table size can be reduced to only a small percent of the table size needed to store all the arithmetic coefficients. We also propose techniques to reduce table size further and to improve performance.