Composite Iterative Algorithm and Architecture for q-th Root Calculation

2011 IEEE 20th Symposium on Computer Arithmetic Pub Date : 2011-07-25 DOI:10.1109/ARITH.2011.16

Álvaro Vázquez, J. Bruguera

引用次数: 12

Abstract

An algorithm for the q-th root extraction, q being any integer, is presented in this paper. The algorithm is based on an optimized implementation of X^{1/q} by a sequence of parallel and/or overlapped operations: (1) reciprocal, (2) digit-recurrence logarithm, (3) left-to-right carry-free multiplication and (4) on-line exponential. A detailed error analysis and two architectures are proposed, for low precision q and for higher precision q. The execution time and hardware requirements are estimated for single precision floating-point computations for several radices, this helps to determine which radices result in the most efficient implementations. The architectures proposed improve the features of other architectures for q-th root extraction.

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q次方根计算的复合迭代算法与体系结构

本文提出了一种q为任意整数时的第q次根提取算法。该算法基于X^{1/q}的优化实现，通过一系列并行和/或重叠操作:(1)倒数，(2)数字递归对数，(3)从左到右无进位乘法和(4)在线指数。对低精度q和高精度q进行了详细的误差分析，并提出了两种架构。对多个基数的单精度浮点计算的执行时间和硬件需求进行了估计，这有助于确定哪种基数产生最有效的实现。所提出的体系结构改进了其他体系结构在q次根提取方面的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2011 IEEE 20th Symposium on Computer Arithmetic

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